[Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated by smorel394 · Pull Request #20255 · leanprover-community/mathlib4

smorel394 · 2024-12-26T13:35:10Z

If a functor F : C ⥤ D between pretriangulated categories is triangulated, and if we
have an adjunction F ⊣ G, then G is also a triangulated functor.

We deduce that, if E : C ≌ D is an equivalence of pretriangulated categories, then
E.functor is triangulated if and only if E.inverse is triangulated.

TODO: The case of left adjoints.

depends on: [Merged by Bors] - feat(CategoryTheory/Adjunction/Additive): adjunctions between additive functors #20083 [the adjoint of an additive functor is additive]
depends on: [Merged by Bors] - feat(CategoryTheory/Shift/Adjunction): properties of Adjunction.CommShift #20337

github-actions · 2024-12-26T13:36:00Z

PR summary 26bcbce653

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
`Mathlib.CategoryTheory.Triangulated.Adjunction` (new file)	1105

Declarations diff

+ comp
+ id
+ instance [E.IsTriangulated] : E.functor.IsTriangulated := inferInstance
+ instance [E.IsTriangulated] : E.inverse.IsTriangulated := inferInstance
+ instance [h : E.functor.IsTriangulated] : E.symm.inverse.IsTriangulated := h
+ instance [h : E.inverse.IsTriangulated] : E.symm.functor.IsTriangulated := h
+ isTriangulated_rightAdjoint
+ mk''
+ refl
+ symm
+ trans
++ IsTriangulated
++ mk'

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.

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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).

Mathlib/CategoryTheory/Triangulated/Adjunction.lean

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

…r-community/mathlib4 into SM.adjointTriangulated

Mathlib/CategoryTheory/Triangulated/Adjunction.lean

mathlib4-dependent-issues-bot · 2025-01-06T13:24:08Z

This PR/issue depends on:

~~[Merged by Bors] - feat(CategoryTheory/Adjunction/Additive): adjunctions between additive functors #20083~~
~~[Merged by Bors] - feat(CategoryTheory/Shift/Adjunction): properties of Adjunction.CommShift #20337~~
By Dependent Issues (🤖). Happy coding!

Mathlib/CategoryTheory/Triangulated/Adjunction.lean

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

joelriou · 2025-01-07T06:58:11Z

As I wrote the original code, there should be a second look:

maintainer merge

github-actions · 2025-01-07T06:58:29Z

🚀 Pull request has been placed on the maintainer queue by joelriou.

TwoFX

Thanks!
bors r+

…triangulated functor is triangulated (#20255) If a functor `F : C ⥤ D` between pretriangulated categories is triangulated, and if we have an adjunction `F ⊣ G`, then `G` is also a triangulated functor. We deduce that, if `E : C ≌ D` is an equivalence of pretriangulated categories, then `E.functor` is triangulated if and only if `E.inverse` is triangulated. TODO: The case of left adjoints. - [x] depends on: #20083 [the adjoint of an additive functor is additive] - [ ] depends on: #20337 Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>

mathlib-bors · 2025-01-07T10:02:16Z

Pull request successfully merged into master.

Build succeeded:

* origin/master: (642 commits) feat: the Boolean subalgebra generated by the lattice generated by a set (#20440) feat: misc. lemmas about moments, tilted measures (#20150) chore(Algebra/Lie): make IsNilpotent and IsSolvable independent of scalars (#20556) feat(Combinatorics/SimpleGraph/Path): add `IsPath.getVert_injOn` (#19373) feat(Combinatorics/SimpleGraph): add lemmas about `spanningCoe` (#19377) chore: scope 'on' notation to Function (#20562) chore: disable docPrime linter (#20559) chore: deprecate MulRingNorm._ in favour of AbsoluteValue._ (#20557) fix(scripts/bench_summary): input jobID as a Nat, rather than a String (#20539) chore: move results about `DivisionMonoid` + `HasDistribNeg` (#20551) feat(NumberTheory/NumberField/Embeddings): definition of totally real field (#20542) chore(Noetherian/Artinian): generalize to Semiring (#20534) chore: protect `Filter.nhds_{iInf,inf}` (#20530) chore(AlgebraicTopology): move SplitSimplicialObject.lean (#20511) chore: extract 3 new files out of MeasureSpace (#20509) feat(RingTheory): Jacobian criterion for smoothness of local algebras (#20326) doc(RingTheory/Flat): add reference to Lambek's paper (#20266) feat(NumberTheory/AbelSummation): add more results (#19942) chore(Multilinear/Basic): generalize the `SMul` instance (#20536) feat(FDeriv/Equiv): generalize `HasFDerivAt.of_local_left_inverse` (#20516) feat(ContDiff): add `iteratedFDeriv_comp` (#20472) feat(LowerUpperTopology): add lemmas (#20465) feat(ContDiff): weaken some assumptions (#20368) fix(scripts/technical-debt-metric): avoid division by 0 (#20537) chore(Algebra/Ring): Clean up in SumsOfSquares and Semireal/Defs (#20528) feat(FTaylorSeries): add lemmas about `dist` between 0th and 1st derivs (#20089) feat: results on inner regularity of finite measures (#19780) chore: to_additive various results on groups, group actions (#20547) feat(Probability/Kernel): `Kernel.sectL` and `sectR` (#15466) chore(CategoryTheory/Limits/Fubini): relax universes constraints and weaken hypotheses (#20553) perf: remove `@[simp]` on `Fintype.card_of{IsEmpty,Subsingleton}` (#20524) fix(HashCommandLinter): remove unnecessary, broken workaround for tests (#20529) chore(Ideal/Basic): dependent generalization of `Ideal.pi` (#20535) feat(RingTheory): being unramified is a local property (#20323) chore(BooleanSubalgebra): use `IsSublattice` in `closure_sdiff_sup_induction` (#20439) feat(Order/SuccPred/CompleteLinearOrder): `⨆ a < x, succ a = x` (#19970) chore(*): replace `no_index (ofNat n)` with `ofNat(n)` everywhere (#20521) feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated (#20255) chore(Order/SuccPred/LinearLocallyFinite): change data-creating instances to defs (#20235) chore: don't import algebra in `Data.Finset.Basic` (#19779) feat: initial segment commutes with `Iio` (#20503) chore(Measure/Pi): move parts to `MeasurableSpace/` (#20215) chore: smile more often (#20436) chore(Algebra/Category/MonCat/ForgetCorepresentable, Algebra/Group/Equiv/Basic): move definitions and add symmetric version (#20416) feat(GroupTheory/QuotientGroup): group correspondence theorem (#20007) doc: change "module homomorphism" to "linear map" (#20481) perf: improves the performance of the `Repr (Equiv.Perm α)` instance (1/4) (#20519) fix: do not keep only the first line of hints (#19756) feat(Analysis/Analytic): lemmas about `smul` for power series (#19816) chore: don't import algebra in `Data.Multiset.Basic` (#19775) ...

* origin/master: (80 commits) chore(CategoryTheory): remove data produced by tactic block (#20565) feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ` (#20540) feat: the Boolean subalgebra generated by the lattice generated by a set (#20440) feat: misc. lemmas about moments, tilted measures (#20150) chore(Algebra/Lie): make IsNilpotent and IsSolvable independent of scalars (#20556) feat(Combinatorics/SimpleGraph/Path): add `IsPath.getVert_injOn` (#19373) feat(Combinatorics/SimpleGraph): add lemmas about `spanningCoe` (#19377) chore: scope 'on' notation to Function (#20562) chore: disable docPrime linter (#20559) chore: deprecate MulRingNorm._ in favour of AbsoluteValue._ (#20557) fix(scripts/bench_summary): input jobID as a Nat, rather than a String (#20539) chore: move results about `DivisionMonoid` + `HasDistribNeg` (#20551) feat(NumberTheory/NumberField/Embeddings): definition of totally real field (#20542) chore(Noetherian/Artinian): generalize to Semiring (#20534) chore: protect `Filter.nhds_{iInf,inf}` (#20530) chore(AlgebraicTopology): move SplitSimplicialObject.lean (#20511) chore: extract 3 new files out of MeasureSpace (#20509) feat(RingTheory): Jacobian criterion for smoothness of local algebras (#20326) doc(RingTheory/Flat): add reference to Lambek's paper (#20266) feat(NumberTheory/AbelSummation): add more results (#19942) chore(Multilinear/Basic): generalize the `SMul` instance (#20536) feat(FDeriv/Equiv): generalize `HasFDerivAt.of_local_left_inverse` (#20516) feat(ContDiff): add `iteratedFDeriv_comp` (#20472) feat(LowerUpperTopology): add lemmas (#20465) feat(ContDiff): weaken some assumptions (#20368) fix(scripts/technical-debt-metric): avoid division by 0 (#20537) chore(Algebra/Ring): Clean up in SumsOfSquares and Semireal/Defs (#20528) feat(FTaylorSeries): add lemmas about `dist` between 0th and 1st derivs (#20089) feat: results on inner regularity of finite measures (#19780) chore: to_additive various results on groups, group actions (#20547) feat(Probability/Kernel): `Kernel.sectL` and `sectR` (#15466) chore(CategoryTheory/Limits/Fubini): relax universes constraints and weaken hypotheses (#20553) perf: remove `@[simp]` on `Fintype.card_of{IsEmpty,Subsingleton}` (#20524) fix(HashCommandLinter): remove unnecessary, broken workaround for tests (#20529) chore(Ideal/Basic): dependent generalization of `Ideal.pi` (#20535) feat(RingTheory): being unramified is a local property (#20323) chore(BooleanSubalgebra): use `IsSublattice` in `closure_sdiff_sup_induction` (#20439) feat(Order/SuccPred/CompleteLinearOrder): `⨆ a < x, succ a = x` (#19970) chore(*): replace `no_index (ofNat n)` with `ofNat(n)` everywhere (#20521) feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated (#20255) chore(Order/SuccPred/LinearLocallyFinite): change data-creating instances to defs (#20235) chore: don't import algebra in `Data.Finset.Basic` (#19779) feat: initial segment commutes with `Iio` (#20503) chore(Measure/Pi): move parts to `MeasurableSpace/` (#20215) chore: smile more often (#20436) chore(Algebra/Category/MonCat/ForgetCorepresentable, Algebra/Group/Equiv/Basic): move definitions and add symmetric version (#20416) feat(GroupTheory/QuotientGroup): group correspondence theorem (#20007) doc: change "module homomorphism" to "linear map" (#20481) perf: improves the performance of the `Repr (Equiv.Perm α)` instance (1/4) (#20519) fix: do not keep only the first line of hints (#19756) ...

morel added 8 commits December 18, 2024 18:49

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Merge remote-tracking branch 'origin' into SM.adjunctionAdditive

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Merge remote-tracking branch 'origin' into SM.adjointTriangulated

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mathlib-bors bot changed the title ~~feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated~~ [Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated Jan 7, 2025

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[Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated#20255

[Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated#20255
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PR summary 26bcbce653

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