[Merged by Bors] - feat: equalizers and coequalizers in the category of ind-objects#21139
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[Merged by Bors] - feat: equalizers and coequalizers in the category of ind-objects#21139
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PR summary 06ea49771aImport changes exceeding 2%
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.CategoryTheory.Limits.Indization.Equalizers | 625 | 638 | +13 (+2.08%) |
| Mathlib.CategoryTheory.Limits.Indization.Category | 660 | 668 | +8 (+1.21%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.CategoryTheory.Generator.Indization Mathlib.CategoryTheory.Limits.Indization.Category |
8 |
Mathlib.CategoryTheory.Limits.Indization.Equalizers |
13 |
Mathlib.CategoryTheory.Limits.Indization.ParallelPair (new file) |
631 |
Declarations diff
+ F₁
+ F₂
+ Ind.exists_nonempty_arrow_mk_iso_ind_lim
+ IndParallelPairPresentation
+ IndParallelPairPresentation.parallelPairIsoParallelPairCompIndYoneda
+ K
+ closedUnderLimitsOfShape_walkingParallelPair_isIndObject
+ hf
+ hg
+ instance [HasColimitsOfShape WalkingParallelPair C] :
+ instance {α : Type w} [SmallCategory α] [FinCategory α] [HasColimitsOfShape α C] {I : Type v}
+ instance {α : Type w} [SmallCategory α] [FinCategory α] [HasLimitsOfShape α C] {I : Type v}
+ isColimit₁
+ isColimit₂
+ nonempty_indParallelPairPresentation
+ parallelPairIsoParallelPairCompYoneda
+ presentation
+ ι₁
+ ι₂
+ ψ
+ ϕ
++ instance {A B : Cᵒᵖ ⥤ Type v₁} {f g : A ⟶ B} (P : IndParallelPairPresentation f g) :
- instance {α : Type v} [SmallCategory α] [FinCategory α] [HasColimitsOfShape α C] {I : Type v}
- instance {α : Type v} [SmallCategory α] [FinCategory α] [HasLimitsOfShape α C] {I : Type v}
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
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).
Contributor
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Thanks! bors merge |
mathlib-bors bot
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Jan 28, 2025
) We study parallel pairs of morphisms in `Ind C`, discover that they are always induced by natural transformations in a suitable indexing category, and deduce that ind-objects are closed under equalizers and the category of ind-objects has coequalizers. Huge thanks to @javra and @datokrat. If they had not spent countless hours tirelessly PRing properties of comma categories and the Grothendieck construction to mathlib this PR would not have been possible, even though you can't see any of their results used in the PR (since they are applied by instance synthesis). Co-authored-by: Markus Himmel <markus@lean-fro.org>
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Pull request successfully merged into master. Build succeeded: |
Julian
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Jan 28, 2025
* origin/master: (294 commits) feat: equalizers and coequalizers in the category of ind-objects (#21139) doc: turn more links to Stacks into `@[stacks]` tags (#21135) feat(Asymptotics): prove `IsLittleOTVS.add` (#20578) feat(Algebra/Polynomial): `Polynomial.aeval` for product algebras (#21062) chore: import Std in Mathlib.lean (#21126) feat(Data/Matroid/Circuit): fundamental circuits and extensionality (#21145) feat(CategoryTheory/Endofunctor): prove the dual form of Lambek's Lemma on terminal coalgebra (#21140) feat(SetTheory/Game/PGame): rewrite left moves of `-x` as right moves of `x` under binders (#21109) feat(RingTheory/Localization/Pi): localization of a finite direct product is a product of localizations (#19042) doc: fixed notation error in customizing category composition (#21132) feat(Matrix): more lemmas for `PEquiv.toMatrix` (#21143) chore(SupIndep): speedup the `Decidable` instance (#21114) fix(CI): use `Elab.async=false` for late importers workflow (#21147) feat(Topology/Algebra/Indicator): indicator of a clopen is continuous (#20687) feat(Data/Matroid/Rank/Cardinal): Cardinality-valued rank function (#20921) feat(Algebra): `Pi.single_induction` (#21141) chore(BigOperators/Fin): golf a proof (#21131) feat: generalize tangent cone lemmas to TVS (#20859) feat(CategoryTheory): `Comma.snd L R` is final if `R` is final and domains are filtered (#21136) refactor: unapply matrix lemmas (#21091) chore(Algebra/Category): `erw` -> `rw` (#21130) feat(CategoryTheory): filteredness of Comma catgories given finality of one of the functors (#21128) feat(Algebra/Category): `ConcreteCategory` instance for `ModuleCat` (#21125) feat: PSum of finite sorts is finite (#20285) feat: inequality on the integral of a convex function of a RN derivative (#21093) feat: `(v +ᵥ s) -ᵥ (v +ᵥ t) = s -ᵥ t` (#21058) chore: rename the fact that `(∀ a < a₁, a ≤ a₂) ↔ a₁ ≤ a₂` in a dense order (#20317) feat: a `RelHom` preserves directedness (#20080) feat(Combinatorics/SimpleGraph): add definitions and theorems about the coloring of sum graphs (#18677) chore(Data/Matrix/PEquiv): clean up names (#21108) feat(Algebra/Category): `ConcreteCategory` instances for rings (#20815) feat: define Descriptive.Tree (#18763) chore(Data/Complex/Exponential): split trig functions to new file (#21075) feat(Logic/IsEmpty/Relator): empty on sides (#20319) feat(Algebra/Category): `ConcreteCategory` instance for `AlgebraCat` (#21121) feat(NumberTheory/LSeries): results involving partial sums of coefficients (part 1) (#20661) feat(RingTheory/LaurentSeries): add algebraEquiv (#21004) chore(SetTheory/Game/Impartial): golf two proofs (#21074) feat(CategoryTheory/Subpresheaf): preimage/image/range of subpresheaves (#21047) feat(RingTheory/IntegralClosure): `Algebra.IsIntegral` transfers via surjective homomorphisms (#21023) feat(`InformationTheory/Hamming`): Add AddGroup instances (#20994) feat(RingTheory/IntegralClosure): prove `Module.Finite R (adjoin R S)` for finite set `S` of integral elements (#20970) feat(RingTheory/Artinian): `IsUnit a` iff `a ∈ R⁰` for an artinian ring `R` (#21084) feat: separating set in the category of ind-objects (#21082) feat: derivWithin lemmas (#21092) chore(Fintype): golf a proof (#21113) chore: golf using `funext₂` (#21106) chore(Algebra/Group/Submonoid/Operations): move instances to new file (#21067) doc(Algebra/BigOperators/Fin): change 'product' to 'sum' in doc-string of additivised declarations (#21101) doc(ComputeDegree): typos (#21095) ...
Julian
added a commit
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Feb 1, 2025
* polynomial-sequences: (308 commits) Use the lemma we already added. Minor reordering. This is true even for the trivial ring. Also add the lt versions and the other inj lemma. Also add the basis ne versions. This seems also like it should be simp. Back to sorry free. And the natDegree version. feat: equalizers and coequalizers in the category of ind-objects (#21139) doc: turn more links to Stacks into `@[stacks]` tags (#21135) feat(Asymptotics): prove `IsLittleOTVS.add` (#20578) feat(Algebra/Polynomial): `Polynomial.aeval` for product algebras (#21062) chore: import Std in Mathlib.lean (#21126) feat(Data/Matroid/Circuit): fundamental circuits and extensionality (#21145) feat(CategoryTheory/Endofunctor): prove the dual form of Lambek's Lemma on terminal coalgebra (#21140) feat(SetTheory/Game/PGame): rewrite left moves of `-x` as right moves of `x` under binders (#21109) feat(RingTheory/Localization/Pi): localization of a finite direct product is a product of localizations (#19042) doc: fixed notation error in customizing category composition (#21132) feat(Matrix): more lemmas for `PEquiv.toMatrix` (#21143) chore(SupIndep): speedup the `Decidable` instance (#21114) fix(CI): use `Elab.async=false` for late importers workflow (#21147) feat(Topology/Algebra/Indicator): indicator of a clopen is continuous (#20687) feat(Data/Matroid/Rank/Cardinal): Cardinality-valued rank function (#20921) feat(Algebra): `Pi.single_induction` (#21141) chore(BigOperators/Fin): golf a proof (#21131) feat: generalize tangent cone lemmas to TVS (#20859) feat(CategoryTheory): `Comma.snd L R` is final if `R` is final and domains are filtered (#21136) refactor: unapply matrix lemmas (#21091) chore(Algebra/Category): `erw` -> `rw` (#21130) feat(CategoryTheory): filteredness of Comma catgories given finality of one of the functors (#21128) feat(Algebra/Category): `ConcreteCategory` instance for `ModuleCat` (#21125) feat: PSum of finite sorts is finite (#20285) feat: inequality on the integral of a convex function of a RN derivative (#21093) feat: `(v +ᵥ s) -ᵥ (v +ᵥ t) = s -ᵥ t` (#21058) chore: rename the fact that `(∀ a < a₁, a ≤ a₂) ↔ a₁ ≤ a₂` in a dense order (#20317) feat: a `RelHom` preserves directedness (#20080) feat(Combinatorics/SimpleGraph): add definitions and theorems about the coloring of sum graphs (#18677) chore(Data/Matrix/PEquiv): clean up names (#21108) feat(Algebra/Category): `ConcreteCategory` instances for rings (#20815) feat: define Descriptive.Tree (#18763) chore(Data/Complex/Exponential): split trig functions to new file (#21075) feat(Logic/IsEmpty/Relator): empty on sides (#20319) feat(Algebra/Category): `ConcreteCategory` instance for `AlgebraCat` (#21121) feat(NumberTheory/LSeries): results involving partial sums of coefficients (part 1) (#20661) feat(RingTheory/LaurentSeries): add algebraEquiv (#21004) chore(SetTheory/Game/Impartial): golf two proofs (#21074) feat(CategoryTheory/Subpresheaf): preimage/image/range of subpresheaves (#21047) feat(RingTheory/IntegralClosure): `Algebra.IsIntegral` transfers via surjective homomorphisms (#21023) feat(`InformationTheory/Hamming`): Add AddGroup instances (#20994) feat(RingTheory/IntegralClosure): prove `Module.Finite R (adjoin R S)` for finite set `S` of integral elements (#20970) ...
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We study parallel pairs of morphisms in
Ind C, discover that they are always induced by natural transformations in a suitable indexing category, and deduce that ind-objects are closed under equalizers and the category of ind-objects has coequalizers.Huge thanks to @javra and @datokrat. If they had not spent countless hours tirelessly PRing properties of comma categories and the Grothendieck construction to mathlib this PR would not have been possible, even though you can't see any of their results used in the PR (since they are applied by instance synthesis).