feat(CategoryTheory): Additive and Linear when Hom types are only monoids#28826
feat(CategoryTheory): Additive and Linear when Hom types are only monoids#28826alreadydone wants to merge 1 commit intoleanprover-community:masterfrom
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| Mathlib.CategoryTheory.Preadditive.Biproducts | 715 | 714 | -1 (-0.14%) |
| Mathlib.CategoryTheory.Preadditive.AdditiveFunctor | 719 | 718 | -1 (-0.14%) |
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98 filesMathlib.Algebra.Category.Grp.Biproducts Mathlib.Algebra.Category.Grp.CartesianMonoidal Mathlib.Algebra.Category.Grp.ChosenFiniteProducts Mathlib.Algebra.Category.Grp.LeftExactFunctor Mathlib.Algebra.Homology.Additive Mathlib.Algebra.Homology.CommSq Mathlib.Algebra.Homology.Embedding.Connect Mathlib.Algebra.Homology.Embedding.RestrictionHomology Mathlib.Algebra.Homology.Embedding.Restriction Mathlib.Algebra.Homology.ExactSequence Mathlib.Algebra.Homology.Factorizations.Basic Mathlib.Algebra.Homology.GrothendieckAbelian Mathlib.Algebra.Homology.HomologicalComplexAbelian Mathlib.Algebra.Homology.HomologicalComplexBiprod Mathlib.Algebra.Homology.HomologySequence Mathlib.Algebra.Homology.Refinements Mathlib.Algebra.Homology.ShortComplex.Abelian Mathlib.Algebra.Homology.ShortComplex.ExactFunctor Mathlib.Algebra.Homology.ShortComplex.Exact Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex Mathlib.Algebra.Homology.ShortComplex.Preadditive Mathlib.Algebra.Homology.ShortComplex.ShortExact Mathlib.Algebra.Homology.ShortComplex.SnakeLemma Mathlib.Algebra.Homology.SingleHomology Mathlib.Algebra.Homology.Square Mathlib.AlgebraicTopology.AlternatingFaceMapComplex Mathlib.AlgebraicTopology.DoldKan.Notations Mathlib.AlgebraicTopology.MooreComplex Mathlib.CategoryTheory.Abelian.Basic Mathlib.CategoryTheory.Abelian.CommSq Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel Mathlib.CategoryTheory.Abelian.Exact Mathlib.CategoryTheory.Abelian.FunctorCategory Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indization Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Types Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Monomorphisms Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject Mathlib.CategoryTheory.Abelian.Indization Mathlib.CategoryTheory.Abelian.Monomorphisms Mathlib.CategoryTheory.Abelian.Opposite Mathlib.CategoryTheory.Abelian.Refinements Mathlib.CategoryTheory.Abelian.SerreClass.Basic Mathlib.CategoryTheory.Abelian.SerreClass.Bousfield Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty Mathlib.CategoryTheory.Abelian.Subobject Mathlib.CategoryTheory.Abelian.Transfer Mathlib.CategoryTheory.Center.Localization Mathlib.CategoryTheory.Distributive.Cartesian Mathlib.CategoryTheory.Distributive.Monoidal Mathlib.CategoryTheory.Generator.Indization Mathlib.CategoryTheory.Idempotents.Basic Mathlib.CategoryTheory.Idempotents.Biproducts Mathlib.CategoryTheory.Idempotents.FunctorCategories Mathlib.CategoryTheory.Idempotents.FunctorExtension Mathlib.CategoryTheory.Idempotents.HomologicalComplex Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi Mathlib.CategoryTheory.Idempotents.Karoubi Mathlib.CategoryTheory.Idempotents.SimplicialObject Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive Mathlib.CategoryTheory.Localization.SmallShiftedHom Mathlib.CategoryTheory.Monoidal.Preadditive Mathlib.CategoryTheory.Noetherian Mathlib.CategoryTheory.ObjectProperty.EpiMono Mathlib.CategoryTheory.ObjectProperty.Extensions Mathlib.CategoryTheory.Preadditive.AdditiveFunctor Mathlib.CategoryTheory.Preadditive.Biproducts Mathlib.CategoryTheory.Preadditive.CommGrp_ Mathlib.CategoryTheory.Preadditive.EilenbergMoore Mathlib.CategoryTheory.Preadditive.EndoFunctor Mathlib.CategoryTheory.Preadditive.Indization Mathlib.CategoryTheory.Preadditive.LeftExact Mathlib.CategoryTheory.Preadditive.Opposite Mathlib.CategoryTheory.Preadditive.Transfer Mathlib.CategoryTheory.Quotient.Preadditive Mathlib.CategoryTheory.Shift.InducedShiftSequence Mathlib.CategoryTheory.Shift.Opposite Mathlib.CategoryTheory.Shift.Pullback Mathlib.CategoryTheory.Shift.ShiftSequence Mathlib.CategoryTheory.Shift.ShiftedHomOpposite Mathlib.CategoryTheory.Shift.ShiftedHom Mathlib.CategoryTheory.Simple Mathlib.CategoryTheory.Sites.Abelian Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits Mathlib.CategoryTheory.Subobject.ArtinianObject Mathlib.CategoryTheory.Subobject.NoetherianObject Mathlib.CategoryTheory.Triangulated.Opposite.Basic Mathlib.CategoryTheory.Triangulated.Opposite.Triangle Mathlib.CategoryTheory.Triangulated.Rotate |
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367 filesMathlib.Algebra.BrauerGroup.Defs Mathlib.Algebra.Category.AlgCat.Basic Mathlib.Algebra.Category.AlgCat.Limits Mathlib.Algebra.Category.AlgCat.Monoidal Mathlib.Algebra.Category.AlgCat.Symmetric Mathlib.Algebra.Category.AlgebraCat.Symmetric Mathlib.Algebra.Category.BialgCat.Basic Mathlib.Algebra.Category.BialgCat.Monoidal Mathlib.Algebra.Category.CoalgCat.Basic Mathlib.Algebra.Category.CoalgCat.ComonEquivalence Mathlib.Algebra.Category.CoalgCat.Monoidal Mathlib.Algebra.Category.CommAlgCat.Basic Mathlib.Algebra.Category.CommAlgCat.FiniteType Mathlib.Algebra.Category.CommAlgCat.Monoidal Mathlib.Algebra.Category.ContinuousCohomology.Basic Mathlib.Algebra.Category.FGModuleCat.Basic Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall Mathlib.Algebra.Category.FGModuleCat.Limits Mathlib.Algebra.Category.Grp.AB Mathlib.Algebra.Category.Grp.Abelian Mathlib.Algebra.Category.Grp.EnoughInjectives Mathlib.Algebra.Category.Grp.Images Mathlib.Algebra.Category.Grp.Injective 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197 filesMathlib.Algebra.Category.Grp.Colimits Mathlib.Algebra.Category.Ring.Constructions Mathlib.Algebra.Category.Ring.Topology Mathlib.Algebra.Category.Ring.Under.Basic Mathlib.Algebra.Homology.BifunctorFlip Mathlib.Algebra.Homology.Bifunctor Mathlib.Algebra.Homology.TotalComplexSymmetry Mathlib.Algebra.Homology.TotalComplex Mathlib.AlgebraicGeometry.AffineScheme Mathlib.AlgebraicGeometry.Cover.MorphismProperty Mathlib.AlgebraicGeometry.Cover.Open Mathlib.AlgebraicGeometry.Cover.Over Mathlib.AlgebraicGeometry.Cover.Sigma Mathlib.AlgebraicGeometry.FunctionField Mathlib.AlgebraicGeometry.GammaSpecAdjunction Mathlib.AlgebraicGeometry.GluingOneHypercover Mathlib.AlgebraicGeometry.Gluing Mathlib.AlgebraicGeometry.IdealSheaf.Basic Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme Mathlib.AlgebraicGeometry.IdealSheaf Mathlib.AlgebraicGeometry.Limits Mathlib.AlgebraicGeometry.Morphisms.AffineAnd Mathlib.AlgebraicGeometry.Morphisms.Affine Mathlib.AlgebraicGeometry.Morphisms.Basic 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Mathlib.AlgebraicGeometry.Pullbacks Mathlib.AlgebraicGeometry.ResidueField Mathlib.AlgebraicGeometry.Restrict Mathlib.AlgebraicGeometry.Scheme Mathlib.AlgebraicGeometry.Sites.BigZariski Mathlib.AlgebraicGeometry.Sites.MorphismProperty Mathlib.AlgebraicGeometry.Sites.Representability Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski Mathlib.AlgebraicGeometry.Sites.Small Mathlib.AlgebraicGeometry.Spec Mathlib.AlgebraicGeometry.SpreadingOut Mathlib.AlgebraicGeometry.Stalk Mathlib.AlgebraicGeometry.StructureSheaf Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.CategoryTheory.Galois.IsFundamentalgroup Mathlib.CategoryTheory.Galois.Topology Mathlib.Condensed.Basic Mathlib.Condensed.CartesianClosed Mathlib.Condensed.Discrete.Basic Mathlib.Condensed.Discrete.Colimit Mathlib.Condensed.Discrete.LocallyConstant Mathlib.Condensed.Equivalence Mathlib.Condensed.Functors Mathlib.Condensed.Light.Basic Mathlib.Condensed.Light.CartesianClosed Mathlib.Condensed.Light.Functors Mathlib.Condensed.Light.TopCatAdjunction Mathlib.Condensed.Light.TopComparison Mathlib.Condensed.TopCatAdjunction Mathlib.Condensed.TopComparison Mathlib.FieldTheory.Laurent Mathlib.FieldTheory.RatFunc.AsPolynomial Mathlib.FieldTheory.RatFunc.Degree Mathlib.Geometry.Manifold.Sheaf.Basic Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace Mathlib.Geometry.Manifold.Sheaf.Smooth Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField Mathlib.Geometry.RingedSpace.LocallyRingedSpace Mathlib.Geometry.RingedSpace.OpenImmersion Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing Mathlib.NumberTheory.ClassNumber.Finite Mathlib.NumberTheory.ClassNumber.FunctionField Mathlib.NumberTheory.Cyclotomic.Basic Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.Gal Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots Mathlib.NumberTheory.Cyclotomic.Rat Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.FunctionField Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.LucasLehmer Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.Basic Mathlib.NumberTheory.NumberField.CMField Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Discriminant.Defs Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.FractionalIdeal Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal.Basic Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind Mathlib.NumberTheory.NumberField.Ideal Mathlib.NumberTheory.NumberField.InfinitePlace.Basic Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex Mathlib.NumberTheory.NumberField.Norm Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.PrimesCongruentOne Mathlib.NumberTheory.RamificationInertia.Basic Mathlib.NumberTheory.RamificationInertia.Galois Mathlib.RingTheory.DedekindDomain.AdicValuation Mathlib.RingTheory.DedekindDomain.Dvr Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing Mathlib.RingTheory.DedekindDomain.Instances Mathlib.RingTheory.DedekindDomain.IntegralClosure Mathlib.RingTheory.DedekindDomain.PID Mathlib.RingTheory.DedekindDomain.SInteger Mathlib.RingTheory.DedekindDomain.SelmerGroup Mathlib.RingTheory.FractionalIdeal.Norm Mathlib.RingTheory.Ideal.Int Mathlib.RingTheory.Ideal.Norm.AbsNorm Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.RingTheory.Invariant.Basic Mathlib.RingTheory.Invariant.Profinite Mathlib.RingTheory.Invariant Mathlib.RingTheory.KrullDimension.Module Mathlib.RingTheory.LaurentSeries Mathlib.RingTheory.LittleWedderburn Mathlib.RingTheory.LocalProperties.Basic Mathlib.RingTheory.LocalProperties.IntegrallyClosed Mathlib.RingTheory.LocalProperties.Reduced Mathlib.RingTheory.Localization.Finiteness Mathlib.RingTheory.Localization.Free Mathlib.RingTheory.Polynomial.Cyclotomic.Basic Mathlib.RingTheory.Polynomial.Cyclotomic.Eval Mathlib.RingTheory.Polynomial.Cyclotomic.Expand Mathlib.RingTheory.Polynomial.Cyclotomic.Roots Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral Mathlib.RingTheory.RingHom.FinitePresentation Mathlib.RingTheory.RingHom.FiniteType Mathlib.RingTheory.RingHom.Finite Mathlib.RingTheory.RingHom.Injective Mathlib.RingTheory.RingHom.Integral Mathlib.RingTheory.RingHom.Locally Mathlib.RingTheory.RingHom.OpenImmersion Mathlib.RingTheory.RingHom.StandardSmooth Mathlib.RingTheory.RingHom.Surjective Mathlib.RingTheory.RingHomProperties Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.Spectrum.Prime.Module Mathlib.RingTheory.Support Mathlib.RingTheory.Trace.Quotient Mathlib.RingTheory.Valuation.Discrete.Basic Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic Mathlib.Topology.Algebra.Valued.WithVal Mathlib.Topology.Category.CompHaus.EffectiveEpi Mathlib.Topology.Category.LightProfinite.EffectiveEpi Mathlib.Topology.Category.Profinite.EffectiveEpi Mathlib.Topology.Category.Stonean.EffectiveEpi Mathlib.Topology.Sheaves.CommRingCat |
2 |
Mathlib.CategoryTheory.Preadditive.Semi (new file) |
618 |
Mathlib.Algebra.Category.MonCat.Presemiadditive (new file) |
626 |
Mathlib.Algebra.Category.ModuleCat.Semi (new file) |
780 |
Declarations diff
+ Hom
+ Hom.Simps.hom
+ Hom.hom
+ Hom.hom₂
+ Hom.hom₂_ofHom₂
+ Hom.instModule
+ Iso.conj_eq_conj
+ Iso.homCongr_eq_arrowCongr
+ LinearEquiv.toModuleIso
+ LinearMap.comp_id_moduleCat
+ LinearMap.id_moduleCat_comp
+ Presemiadditive
+ SemimoduleCat
+ coe_of
+ comp_apply
+ comp_left_eq_zero
+ comp_nsmul
+ comp_right_eq_zero
+ comp_sum
+ endSemiringEquiv
+ forget_map
+ forget_obj
+ forget₂_map
+ forget₂_map_homMk
+ forget₂_obj
+ forget₂_obj_moduleCat_of
+ fullSubcategory
+ hasForgetToAddCommMonoid
+ homEquiv
+ homLinearEquiv
+ homMk
+ hom_add_apply
+ hom_bijective
+ hom_comp
+ hom_ext
+ hom_id
+ hom_injective
+ hom_inv_apply
+ hom_ofHom
+ hom_smul
+ hom_sum
+ hom_surjective
+ hom_zsmul
+ id_apply
+ inducedCategory
+ instPresemiadditive_injective
+ instance (P Q : AddCommMonCat) : AddCommMonoid (P ⟶ Q)
+ instance (X : C) : AddCommMonoid (End X) := inferInstanceAs (AddCommMonoid (X ⟶ X))
+ instance : (forget (SemimoduleCat.{v} R)).ReflectsIsomorphisms
+ instance : (forget₂ (SemimoduleCat.{v} R) AddCommMonCat).Additive
+ instance : (forget₂ (SemimoduleCat.{v} R) AddCommMonCat.{v}).ReflectsIsomorphisms
+ instance : AddCommMonoid (M ⟶ N)
+ instance : AddCommMonoid (mkOfSMul' φ) := by
+ instance : CoeSort (SemimoduleCat.{v} R) (Type v)
+ instance : ConcreteCategory (SemimoduleCat.{v} R) (· →ₗ[R] ·)
+ instance : Functor.Additive (AdditiveFunctor.forget C D)
+ instance : HasZeroMorphisms (SemimoduleCat.{v} R)
+ instance : HasZeroObject (SemimoduleCat.{v} R)
+ instance : Inhabited (SemimoduleCat R)
+ instance : Linear S (SemimoduleCat.{v} S) := SemimoduleCat.Algebra.instLinear
+ instance : Module R (mkOfSMul' φ)
+ instance : Presemiadditive (C ⥤ D)
+ instance : Presemiadditive (C ⥤+ D)
+ instance : Presemiadditive (SemimoduleCat.{v} R)
+ instance : Presemiadditive AddCommMonCat
+ instance : SMul R (mkOfSMul' φ) := ⟨fun r (x : A) => (show A ⟶ A from φ r) x⟩
+ instance : SMul S (M ⟶ N)
+ instance [Preadditive C] : Presemiadditive C
+ instance [Preadditive D] : Preadditive (C ⥤+ D) := .inducedCategory _
+ inv_hom_apply
+ isZero_iff_subsingleton
+ isZero_of_iff_subsingleton
+ isZero_of_subsingleton
+ leftComp
+ linearEquivIsoModuleIso
+ mkOfSMul
+ mkOfSMul'
+ mkOfSMul'_smul
+ mkOfSMul_smul
+ moduleCategory
+ nsmul_comp
+ of
+ ofHom
+ ofHom_apply
+ ofHom_comp
+ ofHom_hom
+ ofHom_id
+ ofHom₂
+ ofHom₂_hom₂
+ ofSelfIso
+ of_coe
+ rightComp
+ smul
+ smulNatTrans
+ smul_naturality
+ subsingleton_of_isZero
+ subsingleton_presemiadditive_of_hasBinaryBiproducts
+ sum_comp
+ sum_comp'
+ toLinearEquiv
++ homAddEquiv
++ hom_add
++ hom_nsmul
++ hom_zero
++ instance : Add (M ⟶ N)
++ instance : Zero (M ⟶ N)
+++ instance : SMul ℕ (M ⟶ N)
+-+ compHom
- instance : Functor.Additive (AdditiveFunctor.forget C D) where map_add := rfl
- instance : Preadditive (C ⥤+ D)
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.
Decrease in tech debt: (relative, absolute) = (1.00, 0.00)
| Current number | Change | Type |
|---|---|---|
| 791 | -1 | erw |
Current commit eb89360f52
Reference commit 3b097993a0
You can run this locally as
./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
079f8ed to
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This pull request has conflicts, please merge |
If you start from a module that is a group then the group structure coming from the ring will not be defeq to the original one. I don't know how much trouble this will cause but I'd rather not deal with it for now. |
SemimoduleCat…anprover-community#31023) + Introduce SemimoduleCat, the category of semimodules (mathlib's Module) over a Semiring. The new file ModuleCat/Semi.lean is copied from ModuleCat/Basic.lean. The additive/linear instances would require leanprover-community#28826.
introduce Presemiadditive categories, which generalizes Preadditive categories: the Hom sets are commutative monoids rather than groups, and
comp_zeroandzero_compis no longer automatic. The new file Preadditive/Semi.lean is adapted from Preadditive/Basic.lean, though many contents can't be generalized.generalize Functor.Additive and Functor.Linear to take Presemiadditive categories instead. The former needs a
map_zerofield since it's not automatic for Presemiadditive categories.introduce SemimoduleCat, the category of semimodules (mathlib's Module) over a Semiring. The new file ModuleCat/Semi.lean is copied from ModuleCat/Basic.lean.
TODOs: additive/linear equivalence between SemimoduleCat and ModuleCat and use it to transfer results; monoidal structure on SemimoduleCat; change
CommRing.Picto use SemimoduleCat.