Skip to content

[Merged by Bors] - feat(CategoryTheory): left and right lifting properties#19135

Closed
mckoen wants to merge 20 commits intomasterfrom
mckoen/lifting
Closed

[Merged by Bors] - feat(CategoryTheory): left and right lifting properties#19135
mckoen wants to merge 20 commits intomasterfrom
mckoen/lifting

Conversation

@mckoen
Copy link
Copy Markdown
Collaborator

@mckoen mckoen commented Nov 16, 2024

Defines left/right lifting property wrt a MorphismProperty and shows basic closure properties (retracts, pullback/pushout, composition etc.).


Open in Gitpod

@mckoen mckoen added WIP Work in progress t-category-theory Category theory labels Nov 16, 2024
@github-actions
Copy link
Copy Markdown

github-actions bot commented Nov 16, 2024

PR summary 2ee843a3b2

Import changes exceeding 2%

% File
+2.30% Mathlib.CategoryTheory.LiftingProperties.Basic

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.CategoryTheory.LiftingProperties.Basic 305 312 +7 (+2.30%)
Import changes for all files
Files Import difference
983 files Mathlib.Algebra.Homology.ShortComplex.Ab Mathlib.Algebra.Homology.ShortComplex.LeftHomology Mathlib.CategoryTheory.Galois.IsFundamentalgroup Mathlib.Topology.Category.Stonean.Adjunctions Mathlib.RingTheory.FractionalIdeal.Norm Mathlib.CategoryTheory.Preadditive.Yoneda.Projective Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion Mathlib.CategoryTheory.Abelian.Generator Mathlib.AlgebraicGeometry.Modules.Sheaf Mathlib.CategoryTheory.Sites.Coherent.ExtensiveTopology Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian Mathlib.CategoryTheory.Limits.Constructions.Filtered Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equalizer Mathlib.NumberTheory.Cyclotomic.Rat Mathlib.RingTheory.DedekindDomain.Dvr Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric Mathlib.Topology.Category.LightProfinite.EffectiveEpi Mathlib.CategoryTheory.Monad.Algebra Mathlib.CategoryTheory.Sites.Pullback Mathlib.RepresentationTheory.GroupCohomology.Hilbert90 Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject Mathlib.CategoryTheory.Functor.Derived.RightDerived Mathlib.CategoryTheory.Abelian.RightDerived Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits Mathlib.CategoryTheory.Shift.InducedShiftSequence Mathlib.CategoryTheory.Sites.Coherent.Comparison Mathlib.AlgebraicGeometry.Sites.Etale Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four Mathlib.Topology.Category.Stonean.EffectiveEpi Mathlib.Algebra.Category.ModuleCat.Limits Mathlib.Algebra.Homology.ShortComplex.RightHomology Mathlib.CategoryTheory.Abelian.Pseudoelements Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels Mathlib.Algebra.Category.FGModuleCat.Limits Mathlib.CategoryTheory.Limits.Shapes.KernelPair Mathlib.CategoryTheory.Localization.HasLocalization Mathlib.AlgebraicGeometry.Morphisms.Proper Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.CategoryTheory.Shift.Predicate Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.AlgebraicGeometry.Morphisms.Preimmersion Mathlib.Topology.Category.CompHaus.EffectiveEpi Mathlib.CategoryTheory.Sites.EqualizerSheafCondition Mathlib.CategoryTheory.Sites.Sieves Mathlib.Algebra.Category.Grp.Zero Mathlib.Algebra.Category.Grp.EpiMono Mathlib.Algebra.Homology.Opposite Mathlib.CategoryTheory.Sites.SheafHom Mathlib.Algebra.Category.Grp.Subobject Mathlib.CategoryTheory.Action.Continuous Mathlib.Algebra.Category.Grp.AB Mathlib.CategoryTheory.Subobject.Types Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct Mathlib.CategoryTheory.Sites.MorphismProperty Mathlib.AlgebraicTopology.FundamentalGroupoid.PUnit Mathlib.Algebra.Homology.Functor Mathlib.Algebra.Homology.DerivedCategory.HomologySequence Mathlib.Algebra.Homology.ShortComplex.SnakeLemma Mathlib.Analysis.Convex.Birkhoff Mathlib.CategoryTheory.Limits.Cones Mathlib.Algebra.Category.Ring.Instances Mathlib.Algebra.Category.CoalgebraCat.ComonEquivalence Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts Mathlib.Topology.Category.Profinite.CofilteredLimit Mathlib.Condensed.Limits Mathlib.Algebra.Category.Ring.Colimits Mathlib.Algebra.Category.ModuleCat.Abelian Mathlib.CategoryTheory.Limits.Shapes.Kernels Mathlib.CategoryTheory.Limits.TypesFiltered Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic Mathlib.CategoryTheory.Abelian.Ext Mathlib.Algebra.Category.ModuleCat.AB Mathlib.AlgebraicGeometry.Sites.MorphismProperty Mathlib.Topology.Sheaves.Sheaf Mathlib.AlgebraicGeometry.Sites.BigZariski Mathlib.RingTheory.Flat.Basic Mathlib.Algebra.Homology.Additive Mathlib.CategoryTheory.Sites.ChosenFiniteProducts Mathlib.Algebra.Category.ModuleCat.Differentials.Basic Mathlib.CategoryTheory.Abelian.FunctorCategory Mathlib.Condensed.TopComparison Mathlib.CategoryTheory.Localization.Bifunctor Mathlib.Algebra.Category.ModuleCat.Kernels Mathlib.Algebra.Homology.Embedding.HomEquiv Mathlib.CategoryTheory.Functor.KanExtension.Pointwise Mathlib.CategoryTheory.Localization.FiniteProducts Mathlib.CategoryTheory.Limits.Preserves.Yoneda Mathlib.Condensed.Discrete.Basic Mathlib.CategoryTheory.Subobject.Limits Mathlib.Algebra.Homology.TotalComplexSymmetry Mathlib.CategoryTheory.Adjunction.Comma Mathlib.Geometry.Manifold.Sheaf.Basic Mathlib.CategoryTheory.Monoidal.Linear Mathlib.AlgebraicTopology.SimplicialSet.Basic Mathlib.AlgebraicGeometry.Morphisms.Basic Mathlib.CategoryTheory.Subobject.Basic Mathlib.CategoryTheory.Limits.Constructions.Pullbacks Mathlib.CategoryTheory.Quotient.Preadditive Mathlib.RingTheory.Regular.RegularSequence Mathlib.NumberTheory.NumberField.FractionalIdeal Mathlib.RingTheory.TensorProduct.Nontrivial Mathlib.Combinatorics.Hall.Basic Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal Mathlib.AlgebraicGeometry.Morphisms.IsIso Mathlib.AlgebraicGeometry.Modules.Presheaf Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer Mathlib.Algebra.Homology.Embedding.IsSupported Mathlib.Algebra.Category.ModuleCat.ChangeOfRings Mathlib.CategoryTheory.Limits.ConcreteCategory.WithAlgebraicStructures Mathlib.AlgebraicGeometry.PrimeSpectrum.FreeLocus Mathlib.CategoryTheory.Sites.SheafCohomology.Basic Mathlib.CategoryTheory.MorphismProperty.Representable Mathlib.Topology.Category.TopCat.EpiMono Mathlib.Algebra.Category.ModuleCat.Adjunctions Mathlib.Topology.Sheaves.SheafCondition.Sites Mathlib.CategoryTheory.Abelian.Transfer Mathlib.CategoryTheory.Monad.Monadicity Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits Mathlib.CategoryTheory.SingleObj Mathlib.CategoryTheory.ConcreteCategory.EpiMono Mathlib.CategoryTheory.Galois.GaloisObjects Mathlib.Topology.Category.Profinite.Nobeling Mathlib.Algebra.Category.Semigrp.Basic Mathlib.Algebra.Homology.ShortComplex.PreservesHomology Mathlib.Condensed.Light.Explicit Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality Mathlib.CategoryTheory.Preadditive.Yoneda.Basic Mathlib.CategoryTheory.Limits.FinallySmall Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel Mathlib.CategoryTheory.Limits.IsLimit Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc Mathlib.Topology.Category.LightProfinite.Extend Mathlib.CategoryTheory.GlueData Mathlib.CategoryTheory.Bicategory.Kan.Adjunction Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated Mathlib.RingTheory.RingHom.FiniteType Mathlib.CategoryTheory.Sites.Subsheaf Mathlib.CategoryTheory.GradedObject.Monoidal Mathlib.CategoryTheory.Enriched.Basic Mathlib.CategoryTheory.Limits.Preserves.Opposites Mathlib.CategoryTheory.Localization.CalculusOfFractions.ComposableArrows Mathlib.CategoryTheory.Dialectica.Basic Mathlib.CategoryTheory.Sites.Whiskering Mathlib.CategoryTheory.Filtered.Final Mathlib.Topology.Sheaves.CommRingCat Mathlib.Algebra.Homology.ShortComplex.Basic Mathlib.CategoryTheory.Limits.FunctorToTypes Mathlib.CategoryTheory.Sites.Preserves Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric Mathlib.AlgebraicTopology.DoldKan.Homotopies Mathlib.AlgebraicTopology.SimplicialSet.KanComplex Mathlib.CategoryTheory.Triangulated.Pretriangulated Mathlib.Topology.Sheaves.MayerVietoris Mathlib.Algebra.Category.Grp.Abelian Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing Mathlib.CategoryTheory.Action.Limits Mathlib.Topology.Category.CompHausLike.EffectiveEpi Mathlib.CategoryTheory.Sites.EpiMono Mathlib.AlgebraicTopology.CechNerve Mathlib.Algebra.Homology.Single Mathlib.CategoryTheory.Abelian.Opposite Mathlib.Algebra.Category.AlgebraCat.Limits Mathlib.CategoryTheory.Subobject.WellPowered Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers Mathlib.CategoryTheory.Preadditive.Generator Mathlib.Condensed.Explicit Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits Mathlib.RingTheory.Localization.Finiteness Mathlib.Condensed.Module Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap Mathlib.Condensed.Discrete.Characterization Mathlib.AlgebraicTopology.Quasicategory.StrictSegal Mathlib.CategoryTheory.Limits.Indization.LocallySmall Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic Mathlib.CategoryTheory.Preadditive.EilenbergMoore Mathlib.CategoryTheory.Comma.StructuredArrow.Basic Mathlib.Algebra.Category.Grp.Kernels Mathlib.CategoryTheory.Limits.Elements Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback Mathlib.RingTheory.Bialgebra.TensorProduct Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact Mathlib.CategoryTheory.Closed.Ideal Mathlib.Topology.Sheaves.Forget Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.CategoryTheory.Shift.Adjunction Mathlib.RepresentationTheory.GroupCohomology.Resolution Mathlib.Algebra.Homology.HomologicalComplex Mathlib.Condensed.Light.CartesianClosed Mathlib.AlgebraicGeometry.Morphisms.Integral Mathlib.CategoryTheory.Preadditive.Projective Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift Mathlib.CategoryTheory.Sites.Continuous Mathlib.Algebra.Homology.HomotopyCategory.MappingCone Mathlib.CategoryTheory.Comma.Presheaf.Basic Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone Mathlib.CategoryTheory.Localization.Pi Mathlib.AlgebraicGeometry.Noetherian Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties Mathlib.Algebra.Category.ModuleCat.Injective Mathlib.Algebra.Category.ModuleCat.Sheaf Mathlib.CategoryTheory.Adjunction.PartialAdjoint Mathlib.RepresentationTheory.Rep Mathlib.CategoryTheory.Monad.Equalizer Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic Mathlib.RingTheory.RingHom.StandardSmooth Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts Mathlib.CategoryTheory.Localization.Construction Mathlib.CategoryTheory.Monoidal.Center Mathlib.RingTheory.RingHom.Flat Mathlib.CategoryTheory.Filtered.Basic Mathlib.CategoryTheory.Triangulated.Basic Mathlib.CategoryTheory.Localization.SmallShiftedHom Mathlib.CategoryTheory.Limits.Constructions.Over.Connected Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular Mathlib.Algebra.Homology.BifunctorFlip Mathlib.CategoryTheory.Limits.Shapes.Images Mathlib.Algebra.Homology.TotalComplexShift Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty Mathlib.CategoryTheory.Abelian.ProjectiveResolution Mathlib.Algebra.Category.ModuleCat.Sheaf.Free Mathlib.AlgebraicTopology.Quasicategory.Nerve Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat Mathlib.CategoryTheory.Limits.Shapes.Terminal Mathlib.CategoryTheory.Limits.Preserves.Basic Mathlib.CategoryTheory.Limits.Constructions.Over.Products Mathlib.CategoryTheory.Localization.Opposite Mathlib.GroupTheory.FreeGroup.NielsenSchreier Mathlib.CategoryTheory.Limits.Presheaf Mathlib.CategoryTheory.Subobject.FactorThru Mathlib.CategoryTheory.Localization.HomEquiv Mathlib.AlgebraicGeometry.Sites.Small Mathlib.MeasureTheory.Category.MeasCat Mathlib.AlgebraicGeometry.Spec Mathlib.Order.Category.OmegaCompletePartialOrder Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory Mathlib.NumberTheory.Cyclotomic.Three Mathlib.RingTheory.RingHom.Finite Mathlib.RingTheory.Unramified.Field Mathlib.CategoryTheory.Closed.Functor Mathlib.NumberTheory.DirichletCharacter.Orthogonality Mathlib.Topology.Category.Profinite.EffectiveEpi Mathlib.CategoryTheory.Shift.Quotient Mathlib.RingTheory.Regular.IsSMulRegular Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive Mathlib.Geometry.Manifold.PoincareConjecture Mathlib.Algebra.Homology.ShortComplex.ModuleCat Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts Mathlib.AlgebraicGeometry.ResidueField Mathlib.CategoryTheory.Limits.Shapes.RegularMono Mathlib.CategoryTheory.Monoidal.Hopf_ Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective Mathlib.Analysis.Normed.Group.SemiNormedGrp Mathlib.CategoryTheory.Limits.Preserves.Limits Mathlib.RingTheory.Flat.Localization Mathlib.CategoryTheory.Sites.LocallySurjective Mathlib.Topology.Sheaves.LocalPredicate Mathlib.Algebra.Category.MonCat.Adjunctions Mathlib.Algebra.Homology.Square Mathlib.CategoryTheory.GradedObject.Associator Mathlib.CategoryTheory.Action Mathlib.CategoryTheory.Limits.Shapes.End Mathlib.CategoryTheory.Category.Pairwise Mathlib.CategoryTheory.Triangulated.Triangulated Mathlib.CategoryTheory.Enriched.FunctorCategory Mathlib.CategoryTheory.Sites.LocallyFullyFaithful Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers Mathlib.Algebra.Category.ModuleCat.Products Mathlib.AlgebraicGeometry.Over Mathlib.CategoryTheory.Monoidal.Braided.Reflection Mathlib.CategoryTheory.Bicategory.Kan.IsKan Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover Mathlib.Topology.Category.Profinite.AsLimit Mathlib.CategoryTheory.Sites.PreservesSheafification Mathlib.CategoryTheory.Sites.Pretopology Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor Mathlib.CategoryTheory.Comma.StructuredArrow.Small Mathlib.CategoryTheory.Monad.EquivMon Mathlib.AlgebraicGeometry.Pullbacks Mathlib.CategoryTheory.Monoidal.Types.Basic Mathlib.CategoryTheory.Sites.IsSheafOneHypercover Mathlib.CategoryTheory.Sites.Abelian Mathlib.Algebra.Category.ModuleCat.Simple Mathlib.Algebra.Category.MonCat.Limits Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.CategoryTheory.EffectiveEpi.Enough Mathlib.Algebra.Category.Grp.EnoughInjectives Mathlib.CategoryTheory.Abelian.Basic Mathlib.CategoryTheory.Limits.Constructions.EpiMono Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero Mathlib.CategoryTheory.Monad.Types Mathlib.CategoryTheory.Preadditive.OfBiproducts Mathlib.AlgebraicTopology.DoldKan.GammaCompN Mathlib.CategoryTheory.Limits.ColimitLimit Mathlib.CategoryTheory.Sites.Localization Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf Mathlib.CategoryTheory.Limits.Yoneda Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected Mathlib.Condensed.Basic Mathlib.AlgebraicTopology.FundamentalGroupoid.Product Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks Mathlib.CategoryTheory.Enriched.Opposite Mathlib.CategoryTheory.Sites.Closed Mathlib.CategoryTheory.Localization.LocalizerMorphism Mathlib.CategoryTheory.Adjunction.AdjointFunctorTheorems Mathlib.CategoryTheory.Limits.Creates Mathlib.CategoryTheory.Sites.ConstantSheaf Mathlib.Condensed.Light.TopComparison Mathlib.Condensed.Light.TopCatAdjunction Mathlib.CategoryTheory.Closed.FunctorCategory.Groupoid Mathlib.CategoryTheory.Preadditive.Yoneda.Injective Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts Mathlib.CategoryTheory.Monoidal.Bimon_ Mathlib.CategoryTheory.Subterminal Mathlib.Condensed.Discrete.LocallyConstant Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf Mathlib.CategoryTheory.Filtered.Small Mathlib.CategoryTheory.Sites.CompatiblePlus Mathlib.RingTheory.Coalgebra.TensorProduct Mathlib.Algebra.Category.Ring.Epi Mathlib.Algebra.Category.ModuleCat.Pseudofunctor Mathlib.CategoryTheory.Limits.Preserves.Presheaf Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves Mathlib.CategoryTheory.Triangulated.HomologicalFunctor Mathlib.Algebra.Homology.ShortComplex.Homology Mathlib.Topology.Category.TopCat.Limits.Cofiltered Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup Mathlib.Algebra.Category.ModuleCat.Sheaf.ChangeOfRings Mathlib.Algebra.Homology.HomotopyCategory.HomologicalFunctor Mathlib.CategoryTheory.Monad.Comonadicity Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono Mathlib.Algebra.Category.ModuleCat.Biproducts Mathlib.CategoryTheory.Functor.EpiMono Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels Mathlib.CategoryTheory.Monad.Basic Mathlib.Combinatorics.Configuration Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone Mathlib.AlgebraicGeometry.Properties Mathlib.CategoryTheory.ChosenFiniteProducts.Cat Mathlib.RingTheory.Etale.Field Mathlib.CategoryTheory.SmallObject.Construction Mathlib.AlgebraicGeometry.Morphisms.Affine Mathlib.CategoryTheory.Shift.ShiftedHomOpposite Mathlib.AlgebraicTopology.SimplicialSet.Path Mathlib.CategoryTheory.ChosenFiniteProducts.FunctorCategory Mathlib.AlgebraicTopology.SimplicialSet.Monoidal Mathlib.CategoryTheory.Endofunctor.Algebra Mathlib.Order.Category.NonemptyFinLinOrd Mathlib.Algebra.Category.ModuleCat.Subobject Mathlib.AlgebraicGeometry.Morphisms.Immersion Mathlib.CategoryTheory.Localization.Prod Mathlib.CategoryTheory.Monoidal.Internal.Types Mathlib.CategoryTheory.Action.Basic Mathlib.RepresentationTheory.Invariants Mathlib.Combinatorics.SimpleGraph.Ends.Defs Mathlib.CategoryTheory.Adjunction.Triple Mathlib.RingTheory.RingHom.Injective Mathlib.RingTheory.Flat.CategoryTheory Mathlib.CategoryTheory.Action.Monoidal Mathlib.CategoryTheory.Sites.CartesianClosed Mathlib.Condensed.Solid Mathlib.Algebra.Homology.HomotopyCategory.Triangulated Mathlib.CategoryTheory.Monoidal.Types.Coyoneda Mathlib.Algebra.Category.ModuleCat.EnoughInjectives Mathlib.Topology.Category.LightProfinite.AsLimit Mathlib.AlgebraicGeometry.Morphisms.Separated Mathlib.CategoryTheory.Sites.Coherent.Basic Mathlib.Condensed.Discrete.Module Mathlib.CategoryTheory.Sites.LocallyInjective Mathlib.Topology.Category.LightProfinite.Limits Mathlib.Topology.Category.CompHaus.Basic Mathlib.CategoryTheory.Preadditive.Schur Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers Mathlib.Algebra.Category.Ring.LinearAlgebra Mathlib.Geometry.RingedSpace.OpenImmersion Mathlib.CategoryTheory.Limits.Shapes.Diagonal Mathlib.AlgebraicTopology.SingularSet Mathlib.CategoryTheory.Limits.Shapes.SingleObj Mathlib.CategoryTheory.Limits.Indization.Category Mathlib.CategoryTheory.Sites.EffectiveEpimorphic Mathlib.Algebra.Category.CoalgebraCat.Basic Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits Mathlib.Algebra.Homology.ImageToKernel Mathlib.RingTheory.Ideal.Norm.AbsNorm Mathlib.AlgebraicGeometry.RationalMap Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic Mathlib.AlgebraicGeometry.Modules.Tilde Mathlib.Topology.Category.CompHaus.Projective Mathlib.AlgebraicGeometry.Morphisms.Finite Mathlib.Topology.Gluing Mathlib.Algebra.Homology.BifunctorAssociator Mathlib.CategoryTheory.Limits.Shapes.Grothendieck Mathlib.CategoryTheory.Preadditive.Mat Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors Mathlib.FieldTheory.Galois.Profinite Mathlib.Algebra.Homology.HomologicalComplexLimits Mathlib.FieldTheory.LinearDisjoint Mathlib.AlgebraicGeometry.Cover.Over Mathlib.CategoryTheory.DifferentialObject Mathlib.CategoryTheory.Abelian.Refinements Mathlib.CategoryTheory.Monoidal.Mod_ Mathlib.CategoryTheory.Quotient.Linear Mathlib.CategoryTheory.EffectiveEpi.Comp Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ Mathlib.NumberTheory.MulChar.Duality Mathlib.Condensed.Light.Epi Mathlib.Algebra.Homology.ShortComplex.Abelian Mathlib.Algebra.Category.Grp.FilteredColimits Mathlib.CategoryTheory.Noetherian Mathlib.CategoryTheory.GuitartExact.Basic Mathlib.CategoryTheory.Abelian.Injective Mathlib.AlgebraicTopology.SimplicialCategory.SimplicialObject Mathlib.Algebra.Category.GrpWithZero Mathlib.Topology.Category.Profinite.Projective Mathlib.CategoryTheory.Monoidal.Tor Mathlib.CategoryTheory.Preadditive.AdditiveFunctor Mathlib.RepresentationTheory.Character Mathlib.CategoryTheory.Limits.Shapes.Equalizers Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences Mathlib.RingTheory.RingHom.FinitePresentation Mathlib.Algebra.Homology.Embedding.Extend Mathlib.Algebra.Category.Ring.FilteredColimits Mathlib.CategoryTheory.Filtered.Grothendieck Mathlib.Topology.Category.TopCat.OpenNhds Mathlib.Algebra.Category.Grp.Adjunctions Mathlib.Combinatorics.SimpleGraph.Finsubgraph Mathlib.CategoryTheory.Galois.Decomposition Mathlib.NumberTheory.FLT.Three Mathlib.LinearAlgebra.LinearDisjoint Mathlib.Topology.Category.Profinite.Basic Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy Mathlib.CategoryTheory.Abelian.Projective Mathlib.CategoryTheory.Sites.Limits Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.CategoryTheory.Subobject.MonoOver Mathlib.Algebra.Homology.HomotopyCategory.HomComplex Mathlib.CategoryTheory.Grothendieck Mathlib.AlgebraicTopology.TopologicalSimplex Mathlib.Topology.Category.CompHausLike.Basic Mathlib.Geometry.RingedSpace.Basic Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts Mathlib.Algebra.Homology.HomologicalComplexBiprod Mathlib.CategoryTheory.Sites.LeftExact Mathlib.Geometry.Manifold.Sheaf.Smooth Mathlib.Topology.CWComplex Mathlib.Algebra.Homology.HomologicalBicomplex Mathlib.CategoryTheory.Localization.Adjunction Mathlib.Topology.Category.CompHaus.Limits Mathlib.CategoryTheory.Galois.Basic Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer Mathlib.CategoryTheory.Idempotents.SimplicialObject Mathlib.CategoryTheory.Linear.Basic Mathlib.AlgebraicGeometry.SpreadingOut Mathlib.AlgebraicGeometry.StructureSheaf Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive Mathlib.Algebra.Category.Grp.Preadditive Mathlib.RingTheory.RingHom.Integral Mathlib.AlgebraicGeometry.Morphisms.AffineAnd Mathlib.Algebra.Category.ModuleCat.Tannaka Mathlib.AlgebraicGeometry.AffineSpace Mathlib.Algebra.Homology.DerivedCategory.ShortExact Mathlib.CategoryTheory.Category.Cat.Limit Mathlib.Condensed.TopCatAdjunction Mathlib.RingTheory.Flat.FaithfullyFlat Mathlib.Algebra.Homology.HomotopyCategory.Shift Mathlib.CategoryTheory.Sites.Sheaf Mathlib.CategoryTheory.Limits.FullSubcategory Mathlib.Algebra.Homology.ShortComplex.Linear Mathlib.CategoryTheory.Shift.Opposite Mathlib.CategoryTheory.Limits.Opposites Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence Mathlib.CategoryTheory.Adjunction.Evaluation Mathlib.CategoryTheory.Monoidal.Mon_ Mathlib.Algebra.Category.ModuleCat.FilteredColimits Mathlib.CategoryTheory.Limits.Constructions.Over.Basic Mathlib.Algebra.Homology.Monoidal Mathlib.Algebra.Category.Ring.Basic Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory Mathlib.CategoryTheory.Triangulated.Rotate Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper Mathlib.CategoryTheory.Preadditive.Basic Mathlib.Algebra.Category.ModuleCat.Colimits Mathlib.CategoryTheory.Preadditive.SingleObj Mathlib.CategoryTheory.Galois.Topology Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic Mathlib.Algebra.Category.BialgebraCat.Basic Mathlib.CategoryTheory.Limits.ConeCategory Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective Mathlib.AlgebraicGeometry.FunctionField Mathlib.RingTheory.DedekindDomain.Different Mathlib.AlgebraicGeometry.Morphisms.Constructors Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators Mathlib.CategoryTheory.Limits.Indization.Products Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian Mathlib.Topology.Category.TopCat.Opens Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory Mathlib.CategoryTheory.CofilteredSystem Mathlib.AlgebraicTopology.DoldKan.Notations Mathlib.Algebra.Homology.Refinements Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal Mathlib.Algebra.Category.MonCat.Colimits Mathlib.Algebra.Module.PID Mathlib.CategoryTheory.Closed.FunctorCategory.Complete Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence Mathlib.CategoryTheory.Limits.IsConnected Mathlib.Algebra.Category.AlgebraCat.Symmetric Mathlib.CategoryTheory.Limits.Comma Mathlib.Topology.Category.CompactlyGenerated Mathlib.CategoryTheory.Sites.Spaces Mathlib.CategoryTheory.Functor.KanExtension.Adjunction Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts Mathlib.CategoryTheory.Shift.Induced Mathlib.CategoryTheory.Limits.Shapes.Connected Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1 Mathlib.Topology.Category.TopCat.Limits.Konig Mathlib.Topology.Homotopy.HomotopyGroup Mathlib.CategoryTheory.Sites.Coherent.Equivalence Mathlib.AlgebraicTopology.DoldKan.Normalized Mathlib.CategoryTheory.Limits.Preserves.Shapes.Images Mathlib.CategoryTheory.Galois.Full Mathlib.CategoryTheory.Sites.Sheafification Mathlib.AlgebraicTopology.SimplicialNerve Mathlib.CategoryTheory.Limits.Indization.IndObject Mathlib.CategoryTheory.Monoidal.Limits Mathlib.CategoryTheory.Sites.Coverage Mathlib.RingTheory.AdicCompletion.AsTensorProduct Mathlib.Algebra.Category.MonCat.Basic Mathlib.Algebra.Category.ModuleCat.Basic Mathlib.CategoryTheory.Limits.Final.ParallelPair Mathlib.CategoryTheory.Limits.Filtered Mathlib.Algebra.Category.Grp.ForgetCorepresentable Mathlib.Topology.Sheaves.Limits Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology Mathlib.Algebra.Homology.ShortComplex.QuasiIso Mathlib.CategoryTheory.Limits.Shapes.Countable Mathlib.Geometry.RingedSpace.SheafedSpace Mathlib.AlgebraicGeometry.Morphisms.Smooth Mathlib.CategoryTheory.Localization.Triangulated Mathlib.CategoryTheory.Dialectica.Monoidal Mathlib.CategoryTheory.Galois.Prorepresentability Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed Mathlib.CategoryTheory.Triangulated.Opposite Mathlib.CategoryTheory.Abelian.Subobject Mathlib.CategoryTheory.Limits.Shapes.Equivalence Mathlib.Algebra.Homology.ComplexShapeSigns Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup Mathlib.AlgebraicTopology.DoldKan.Faces Mathlib.AlgebraicGeometry.OpenImmersion Mathlib.CategoryTheory.Monoidal.Preadditive Mathlib.CategoryTheory.Monoidal.Internal.Limits Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory Mathlib.CategoryTheory.Limits.SmallComplete Mathlib.Algebra.Category.FGModuleCat.Basic Mathlib.Algebra.Homology.Localization Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct Mathlib.Topology.Sheaves.SheafOfFunctions Mathlib.RingTheory.Localization.Free Mathlib.Algebra.Homology.ShortComplex.Preadditive Mathlib.CategoryTheory.Simple Mathlib.Algebra.Homology.BifunctorHomotopy Mathlib.Geometry.RingedSpace.LocallyRingedSpace Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator Mathlib.Algebra.Homology.ShortComplex.Exact Mathlib.NumberTheory.Cyclotomic.PID Mathlib.CategoryTheory.Preadditive.Injective Mathlib.CategoryTheory.Monad.Limits Mathlib.Topology.Sheaves.LocallySurjective Mathlib.Algebra.Module.CharacterModule Mathlib.CategoryTheory.Monoidal.Rigid.Braided Mathlib.CategoryTheory.Monoidal.Comon_ Mathlib.AlgebraicTopology.DoldKan.Equivalence Mathlib.CategoryTheory.Limits.Fubini Mathlib.CategoryTheory.Idempotents.Basic Mathlib.CategoryTheory.GradedObject.Trifunctor Mathlib.CategoryTheory.Adjunction.Limits Mathlib.Algebra.Category.Grp.FiniteGrp Mathlib.CategoryTheory.Localization.Composition Mathlib.CategoryTheory.Idempotents.FunctorExtension Mathlib.AlgebraicGeometry.AffineScheme Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq Mathlib.Algebra.Category.ModuleCat.Algebra Mathlib.CategoryTheory.Abelian.Images Mathlib.CategoryTheory.Limits.Shapes.Reflexive Mathlib.CategoryTheory.Limits.ExactFunctor Mathlib.CategoryTheory.Sites.Equivalence Mathlib.CategoryTheory.GuitartExact.VerticalComposition Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves Mathlib.Algebra.Category.Grp.Images Mathlib.CategoryTheory.Monoidal.Rigid.Basic Mathlib.AlgebraicTopology.DoldKan.Decomposition Mathlib.Algebra.Category.Grp.ZModuleEquivalence Mathlib.Condensed.Light.AB Mathlib.Algebra.Homology.SingleHomology Mathlib.AlgebraicTopology.SimplexCategory Mathlib.CategoryTheory.GradedObject Mathlib.CategoryTheory.MorphismProperty.Comma Mathlib.CategoryTheory.Sites.Canonical Mathlib.CategoryTheory.Subobject.Comma Mathlib.CategoryTheory.Closed.Types Mathlib.AlgebraicGeometry.Limits Mathlib.AlgebraicTopology.DoldKan.PInfty Mathlib.CategoryTheory.Limits.Shapes.Types Mathlib.Algebra.Category.Ring.Under.Limits Mathlib.CategoryTheory.Sites.CoversTop Mathlib.CategoryTheory.Comma.OverClass Mathlib.CategoryTheory.Shift.SingleFunctors Mathlib.Algebra.Category.Ring.Limits Mathlib.AlgebraicTopology.SimplicialSet.Nerve Mathlib.CategoryTheory.Sites.ConcreteSheafification Mathlib.CategoryTheory.Limits.Shapes.PiProd Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology Mathlib.CategoryTheory.Shift.Localization Mathlib.Topology.Category.Compactum Mathlib.CategoryTheory.Shift.CommShift Mathlib.CategoryTheory.Monoidal.Subcategory Mathlib.CategoryTheory.Adjunction.Over Mathlib.Algebra.Category.AlgebraCat.Monoidal Mathlib.LinearAlgebra.CliffordAlgebra.CategoryTheory Mathlib.AlgebraicTopology.DoldKan.FunctorGamma Mathlib.CategoryTheory.Triangulated.TriangleShift Mathlib.CategoryTheory.Limits.Preserves.Filtered Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts Mathlib.Geometry.RingedSpace.Stalks Mathlib.CategoryTheory.GradedObject.Single Mathlib.Condensed.Light.Limits Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps Mathlib.Algebra.Homology.TotalComplex Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.CategoryTheory.Adjunction.Lifting.Left Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits Mathlib.Condensed.Discrete.Colimit Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic Mathlib.CategoryTheory.Filtered.Connected Mathlib.RepresentationTheory.GroupCohomology.Basic Mathlib.Algebra.Homology.HomologySequenceLemmas Mathlib.Topology.Category.Profinite.Extend Mathlib.RingTheory.RingHom.Locally Mathlib.CategoryTheory.Preadditive.Biproducts Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal Mathlib.RepresentationTheory.FDRep Mathlib.Algebra.Homology.Embedding.Boundary Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.Condensed.CartesianClosed Mathlib.CategoryTheory.Preadditive.ProjectiveResolution Mathlib.CategoryTheory.Limits.IndYoneda Mathlib.Topology.Sheaves.PresheafOfFunctions Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic Mathlib.Topology.Compactness.CompactlyGeneratedSpace Mathlib.RingTheory.Trace.Quotient Mathlib.Topology.Category.Stonean.Basic Mathlib.CategoryTheory.SmallObject.Iteration.UniqueHom Mathlib.CategoryTheory.Monoidal.Internal.Module Mathlib.CategoryTheory.Comma.StructuredArrow.Functor Mathlib.Topology.Algebra.ProperAction.ProperlyDiscontinuous Mathlib.CategoryTheory.EffectiveEpi.Extensive Mathlib.Algebra.Homology.HomologicalComplexAbelian Mathlib.CategoryTheory.Preadditive.LeftExact Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField Mathlib.Algebra.Homology.DifferentialObject Mathlib.Topology.Category.CompHausLike.SigmaComparison Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation Mathlib.Algebra.Category.MonCat.FilteredColimits Mathlib.CategoryTheory.Sites.Subcanonical Mathlib.Topology.Category.TopCat.Limits.Products Mathlib.AlgebraicTopology.SplitSimplicialObject Mathlib.CategoryTheory.Limits.Constructions.Equalizers Mathlib.CategoryTheory.GradedObject.Braiding Mathlib.Topology.Category.LightProfinite.Basic Mathlib.AlgebraicTopology.Quasicategory.Basic Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes Mathlib.CategoryTheory.Limits.Bicones Mathlib.CategoryTheory.EffectiveEpi.Coproduct Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves Mathlib.RingTheory.LocalProperties.Reduced Mathlib.CategoryTheory.GradedObject.Bifunctor Mathlib.CategoryTheory.GradedObject.Unitor Mathlib.CategoryTheory.Idempotents.HomologicalComplex Mathlib.Algebra.Category.AlgebraCat.Basic Mathlib.Algebra.Category.CoalgebraCat.Monoidal Mathlib.Algebra.Homology.LocalCohomology Mathlib.AlgebraicGeometry.Morphisms.FiniteType Mathlib.CategoryTheory.Abelian.Exact Mathlib.Algebra.Category.ModuleCat.Presheaf Mathlib.CategoryTheory.Comma.Final Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion Mathlib.CategoryTheory.Shift.ShiftSequence Mathlib.RingTheory.LocalProperties.IntegrallyClosed Mathlib.CategoryTheory.Monoidal.CommMon_ Mathlib.CategoryTheory.Idempotents.FunctorCategories Mathlib.AlgebraicGeometry.Scheme Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square Mathlib.RingTheory.Flat.EquationalCriterion Mathlib.CategoryTheory.Limits.FunctorCategory.Filtered Mathlib.Topology.Category.LightProfinite.Sequence Mathlib.Algebra.Homology.QuasiIso Mathlib.AlgebraicTopology.DoldKan.NCompGamma Mathlib.Condensed.Light.Basic Mathlib.AlgebraicGeometry.Gluing Mathlib.Topology.Sheaves.Functors Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence Mathlib.CategoryTheory.Closed.Monoidal Mathlib.CategoryTheory.Preadditive.Opposite Mathlib.Algebra.Category.Ring.Under.Basic Mathlib.CategoryTheory.Sites.Over Mathlib.CategoryTheory.Subobject.Lattice Mathlib.RepresentationTheory.GroupCohomology.LowDegree Mathlib.RingTheory.RingHomProperties Mathlib.AlgebraicGeometry.Cover.Open Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit Mathlib.CategoryTheory.Sites.MayerVietorisSquare Mathlib.AlgebraicGeometry.Stalk Mathlib.Condensed.Light.Module Mathlib.Algebra.Category.Ring.Constructions Mathlib.CategoryTheory.Abelian.NonPreadditive Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc Mathlib.CategoryTheory.Monad.Adjunction Mathlib.CategoryTheory.Sites.CoverPreserving Mathlib.Topology.Category.Locale Mathlib.CategoryTheory.Localization.SmallHom Mathlib.Algebra.Category.Grp.Limits Mathlib.CategoryTheory.Limits.EssentiallySmall Mathlib.CategoryTheory.Comma.Over Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso Mathlib.AlgebraicTopology.ExtraDegeneracy Mathlib.GroupTheory.FiniteAbelian.Duality Mathlib.CategoryTheory.Monoidal.Types.Symmetric Mathlib.CategoryTheory.Sites.PreservesLocallyBijective Mathlib.CategoryTheory.Galois.Examples Mathlib.CategoryTheory.Sites.LocallyBijective Mathlib.Topology.Category.CompHausLike.Limits Mathlib.Algebra.Homology.Linear Mathlib.CategoryTheory.Sites.OneHypercover Mathlib.RingTheory.LinearDisjoint Mathlib.CategoryTheory.Category.Factorisation Mathlib.CategoryTheory.Sites.DenseSubsite.Basic Mathlib.CategoryTheory.Sites.Types Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms Mathlib.Algebra.Homology.HomotopyCategory.ShortExact Mathlib.CategoryTheory.Triangulated.Subcategory Mathlib.CategoryTheory.Triangulated.Functor Mathlib.RingTheory.LocalRing.Module Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono Mathlib.CategoryTheory.ConcreteCategory.Elementwise Mathlib.CategoryTheory.Limits.VanKampen Mathlib.Topology.Sheaves.Skyscraper Mathlib.CategoryTheory.Elements Mathlib.CategoryTheory.Abelian.InjectiveResolution Mathlib.CategoryTheory.Triangulated.TStructure.Basic Mathlib.CategoryTheory.Sites.SheafOfTypes Mathlib.CategoryTheory.Abelian.GrothendieckCategory Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts Mathlib.CategoryTheory.Generator Mathlib.CategoryTheory.Limits.Over Mathlib.Algebra.Category.Grp.Biproducts Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso Mathlib.CategoryTheory.Preadditive.InjectiveResolution Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections Mathlib.CategoryTheory.Functor.ReflectsIso Mathlib.CategoryTheory.Preadditive.HomOrthogonal Mathlib.CategoryTheory.Localization.StructuredArrow Mathlib.Algebra.Homology.Embedding.Restriction Mathlib.Algebra.Homology.ExactSequence Mathlib.CategoryTheory.Localization.CalculusOfFractions Mathlib.CategoryTheory.Galois.Action Mathlib.CategoryTheory.Limits.Connected Mathlib.CategoryTheory.Adjunction.Lifting.Right Mathlib.CategoryTheory.Limits.Shapes.IsTerminal Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace Mathlib.CategoryTheory.Functor.FunctorHom Mathlib.Order.Category.Frm Mathlib.RingTheory.LocalProperties.Basic Mathlib.NumberTheory.NumberField.House Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic Mathlib.Algebra.Category.Grp.Colimits Mathlib.CategoryTheory.Limits.Indization.FilteredColimits Mathlib.AlgebraicTopology.AlternatingFaceMapComplex Mathlib.CategoryTheory.Limits.Shapes.StrongEpi Mathlib.CategoryTheory.Abelian.LeftDerived Mathlib.Condensed.Epi Mathlib.CategoryTheory.Limits.Shapes.StrictInitial Mathlib.Topology.Maps.Proper.CompactlyGenerated Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting Mathlib.CategoryTheory.Localization.Predicate Mathlib.CategoryTheory.Limits.Indization.Equalizers Mathlib.AlgebraicGeometry.GammaSpecAdjunction Mathlib.Algebra.Homology.Homotopy Mathlib.CategoryTheory.Linear.LinearFunctor Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects Mathlib.CategoryTheory.MorphismProperty.OverAdjunction Mathlib.RingTheory.Flat.Equalizer Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory Mathlib.CategoryTheory.Extensive Mathlib.Algebra.Homology.CommSq Mathlib.CategoryTheory.Monad.Products Mathlib.AlgebraicTopology.SimplicialObject.Basic Mathlib.CategoryTheory.ChosenFiniteProducts Mathlib.CategoryTheory.Limits.Constructions.WeaklyInitial Mathlib.CategoryTheory.Enriched.HomCongr Mathlib.CategoryTheory.Limits.MorphismProperty Mathlib.Topology.Sheaves.PUnit Mathlib.Algebra.Category.ModuleCat.Free Mathlib.CategoryTheory.Monad.Coequalizer Mathlib.AlgebraicTopology.MooreComplex Mathlib.Condensed.Light.Functors Mathlib.GroupTheory.FiniteAbelian.Basic Mathlib.AlgebraicGeometry.Cover.MorphismProperty Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks Mathlib.Topology.Sheaves.Presheaf Mathlib.CategoryTheory.Adhesive Mathlib.CategoryTheory.Limits.HasLimits Mathlib.CategoryTheory.Closed.Enrichment Mathlib.CategoryTheory.Limits.Shapes.Biproducts Mathlib.AlgebraicGeometry.GluingOneHypercover Mathlib.Algebra.Category.MonCat.ForgetCorepresentable Mathlib.CategoryTheory.Functor.KanExtension.Basic Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic Mathlib.CategoryTheory.Closed.Zero Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory Mathlib.CategoryTheory.SmallObject.Iteration.Basic Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat Mathlib.CategoryTheory.Closed.FunctorToTypes Mathlib.Algebra.Homology.Bifunctor Mathlib.Topology.Category.TopCat.Limits.Basic Mathlib.CategoryTheory.Limits.Lattice Mathlib.AlgebraicGeometry.ValuativeCriterion Mathlib.AlgebraicGeometry.Restrict Mathlib.AlgebraicGeometry.PullbackCarrier Mathlib.Algebra.Category.ModuleCat.Projective Mathlib.Algebra.Category.Grp.Basic Mathlib.Algebra.Homology.HomotopyCofiber Mathlib.Algebra.Homology.Augment Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv Mathlib.RingTheory.Flat.Stability Mathlib.CategoryTheory.Limits.FintypeCat Mathlib.CategoryTheory.Sites.Adjunction Mathlib.Condensed.Functors Mathlib.Algebra.Category.ModuleCat.Images Mathlib.CategoryTheory.Limits.Pi Mathlib.CategoryTheory.Idempotents.Karoubi Mathlib.CategoryTheory.EffectiveEpi.Preserves Mathlib.CategoryTheory.Limits.EpiMono Mathlib.Topology.Category.TopCat.Yoneda Mathlib.CategoryTheory.Limits.Preserves.Ulift Mathlib.CategoryTheory.Monoidal.Bimod Mathlib.Topology.Category.TopCommRingCat Mathlib.CategoryTheory.Adjunction.Reflective Mathlib.CategoryTheory.Bicategory.Extension Mathlib.Condensed.Equivalence Mathlib.CategoryTheory.Sites.IsSheafFor Mathlib.CategoryTheory.EffectiveEpi.Basic Mathlib.CategoryTheory.Closed.Cartesian Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal Mathlib.Topology.Category.Profinite.Product Mathlib.CategoryTheory.Idempotents.Biproducts Mathlib.Topology.Category.Profinite.Limits Mathlib.CategoryTheory.Galois.EssSurj Mathlib.Topology.Category.UniformSpace Mathlib.CategoryTheory.Linear.Yoneda Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.CategoryTheory.Sites.Coherent.SheafComparison Mathlib.CategoryTheory.Preadditive.EndoFunctor Mathlib.Algebra.Homology.HomologySequence Mathlib.CategoryTheory.Comma.Presheaf.Colimit Mathlib.Geometry.RingedSpace.PresheafedSpace Mathlib.CategoryTheory.Shift.Basic Mathlib.CategoryTheory.Category.Grpd Mathlib.CategoryTheory.LiftingProperties.Adjunction Mathlib.CategoryTheory.Limits.Preserves.Finite Mathlib.Algebra.Category.ModuleCat.Presheaf.Abelian Mathlib.CategoryTheory.Preadditive.FunctorCategory Mathlib.RingTheory.RingHom.Surjective Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting Mathlib.CategoryTheory.Limits.Unit Mathlib.RingTheory.DedekindDomain.PID Mathlib.Algebra.Category.Grp.Injective Mathlib.Algebra.Category.BoolRing Mathlib.AlgebraicTopology.SimplicialCategory.Basic Mathlib.Topology.Category.TopCat.EffectiveEpi Mathlib.CategoryTheory.Linear.FunctorCategory Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed Mathlib.CategoryTheory.Action.Concrete Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.Algebra.Homology.ShortComplex.ShortExact Mathlib.CategoryTheory.Localization.Resolution Mathlib.Algebra.Category.Ring.Adjunctions Mathlib.Algebra.Homology.HomotopyCategory Mathlib.CategoryTheory.Limits.Shapes.Products Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous Mathlib.Algebra.Homology.ShortComplex.Limits Mathlib.Topology.Sheaves.Sheafify Mathlib.RingTheory.Unramified.Finite Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit Mathlib.CategoryTheory.MorphismProperty.Limits Mathlib.Algebra.Category.HopfAlgebraCat.Basic Mathlib.CategoryTheory.FiberedCategory.BasedCategory Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent Mathlib.CategoryTheory.Triangulated.Yoneda Mathlib.CategoryTheory.Localization.Equivalence Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct Mathlib.CategoryTheory.Functor.Flat Mathlib.CategoryTheory.Monoidal.Conv Mathlib.AlgebraicTopology.DoldKan.FunctorN Mathlib.CategoryTheory.Shift.ShiftedHom Mathlib.Algebra.Homology.BifunctorShift Mathlib.CategoryTheory.EffectiveEpi.RegularEpi Mathlib.Topology.Order.Category.FrameAdjunction Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits Mathlib.CategoryTheory.Limits.FunctorCategory.Finite Mathlib.CategoryTheory.Sites.Coherent.ReflectsPrecoherent Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.Algebra.Homology.ShortComplex.ExactFunctor Mathlib.CategoryTheory.Bicategory.Kan.HasKan Mathlib.Algebra.Homology.Embedding.StupidTrunc Mathlib.CategoryTheory.Sites.Grothendieck Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings Mathlib.Topology.Sheaves.Stalks Mathlib.CategoryTheory.Sites.Plus Mathlib.CategoryTheory.Limits.Final Mathlib.CategoryTheory.Shift.Pullback Mathlib.CategoryTheory.Enriched.Ordinary Mathlib.Algebra.Category.ModuleCat.EpiMono Mathlib.Algebra.Homology.DerivedCategory.Basic Mathlib.Algebra.Homology.ConcreteCategory Mathlib.CategoryTheory.Sites.CompatibleSheafification Mathlib.CategoryTheory.Monad.Kleisli Mathlib.Algebra.Homology.Factorizations.Basic Mathlib.CategoryTheory.WithTerminal Mathlib.Combinatorics.SimpleGraph.Ends.Properties Mathlib.CategoryTheory.Localization.Bousfield Mathlib.CategoryTheory.Preadditive.Yoneda.Limits Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor Mathlib.CategoryTheory.Limits.Types Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.CategoryTheory.Sites.Coherent.RegularTopology Mathlib.Algebra.Homology.Embedding.ExtendHomology Mathlib.Topology.Category.TopCat.Limits.Pullbacks Mathlib.Topology.Category.Stonean.Limits Mathlib.AlgebraicTopology.DoldKan.NReflectsIso Mathlib.AlgebraicGeometry.Morphisms.Etale Mathlib.CategoryTheory.Limits.Sifted Mathlib.Algebra.Homology.DerivedCategory.Ext.ExtClass Mathlib.AlgebraicTopology.DoldKan.Degeneracies Mathlib.CategoryTheory.Limits.MonoCoprod Mathlib.Algebra.Category.ModuleCat.Presheaf.Free Mathlib.AlgebraicTopology.DoldKan.Projections Mathlib.CategoryTheory.Limits.FunctorCategory.Basic Mathlib.Algebra.Homology.Embedding.TruncGE Mathlib.CategoryTheory.Filtered.OfColimitCommutesFiniteLimit Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit Mathlib.CategoryTheory.Sites.CoverLifting
1
Mathlib.CategoryTheory.LiftingProperties.Basic 7
Mathlib.CategoryTheory.LiftingProperties.Limits (new file) 576
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty (new file) 591

Declarations diff

+ IsPullback.hasLiftingProperty
+ IsPushout.hasLiftingProperty
+ IsStableUnderCobaseChange.isomorphisms
+ IsStableUnderColimitsOfShape
+ IsStableUnderColimitsOfShape.colim_map
+ IsStableUnderCoproductsOfShape
+ IsStableUnderCoproductsOfShape.mk
+ IsStableUnderFiniteCoproducts
+ RetractArrow.leftLiftingProperty
+ RetractArrow.rightLiftingProperty
+ instance [HasPullback g t] {T₁ T₂ : C} (p : T₁ ⟶ T₂) [HasLiftingProperty p g] :
+ instance [HasPullback g t] {T₁ T₂ : C} (p : T₁ ⟶ T₂) [HasLiftingProperty p t] :
+ instance [HasPushout s f] {T₁ T₂ : C} (p : T₁ ⟶ T₂) [HasLiftingProperty f p] :
+ instance [HasPushout s f] {T₁ T₂ : C} (p : T₁ ⟶ T₂) [HasLiftingProperty s p] :
+ instance {J : Type*} {A B : J → C} [HasCoproduct A] [HasCoproduct B]
+ instance {J : Type*} {A B : J → C} [HasProduct A] [HasProduct B]
+ isStableUnderCoproductsOfShape_of_isStableUnderFiniteCoproducts
+ llp
+ llp_IsStableUnderCoproductsOfShape
+ llp_isMultiplicative
+ llp_isStableUnderCobaseChange
+ llp_isStableUnderRetracts
+ rlp
+ rlp_IsStableUnderProductsOfShape
+ rlp_isMultiplicative
+ rlp_isStableUnderBaseChange
+ rlp_isStableUnderRetracts

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@joelriou
Copy link
Copy Markdown
Contributor

It could be advisable to split this PR into two:

  • one for the basic Retract API
  • one for the improvements to the HasLiftingProperty API I have suggested and the application to rlp/llp.

@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes. label Nov 18, 2024
@mckoen
Copy link
Copy Markdown
Collaborator Author

mckoen commented Nov 18, 2024

It could be advisable to split this PR into two:

* one for the basic `Retract` API

* one for the improvements to the `HasLiftingProperty` API I have suggested and the application to `rlp/llp`.

I think that's a good call. I'll split the PR.

@github-actions github-actions bot added the large-import Automatically added label for PRs with a significant increase in transitive imports label Dec 21, 2024
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes. label Dec 21, 2024
@joelriou joelriou removed the awaiting-author A reviewer has asked the author a question or requested changes. label Dec 22, 2024
@joelriou
Copy link
Copy Markdown
Contributor

Thanks!

bors merge

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Dec 22, 2024
mathlib-bors bot pushed a commit that referenced this pull request Dec 22, 2024
Defines left/right lifting property wrt a `MorphismProperty` and shows basic closure properties (retracts, pullback/pushout, composition etc.).



Co-authored-by: Jack McKoen <104791831+mckoen@users.noreply.github.com>
@mathlib-bors
Copy link
Copy Markdown
Contributor

mathlib-bors bot commented Dec 22, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(CategoryTheory): left and right lifting properties [Merged by Bors] - feat(CategoryTheory): left and right lifting properties Dec 22, 2024
@mathlib-bors mathlib-bors bot closed this Dec 22, 2024
@mathlib-bors mathlib-bors bot deleted the mckoen/lifting branch December 22, 2024 10:15
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

large-import Automatically added label for PRs with a significant increase in transitive imports ready-to-merge This PR has been sent to bors. t-category-theory Category theory

Projects

None yet

Development

Successfully merging this pull request may close these issues.

5 participants