[Merged by Bors] - chore(CategoryTheory/Shift): fix NatTrans.CommShift#20364
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[Merged by Bors] - chore(CategoryTheory/Shift): fix NatTrans.CommShift#20364
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PR summary 3d7431c928Import changes for modified filesNo significant changes to the import graph Import changes for all files
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| 1514 | -2 | erw |
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
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This PR improves some proofs about `NatTrans.CommShift` (the commutation of a natural transformation to shifts). The field `comm'` of `NatTrans.CommShift` had an unnecessary `'` in it, it is renamed `shift_comm`, and API lemmas are moved from `NatTrans.CommShift` to the `NatTrans` namespace (where `comm` becomes `shift_comm` and `comm_app` becomes `shift_app_comm`).
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…Shift` (#20337) Provide instances that say that `Adjunction.CommShift` holds for the identity adjunction and is stable by composition, as well as similar instances for `Equivalence.CommShift`. - [ ] depends on: #20364 - [ ] depends on: #20490 Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com> Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>
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…: `CommShift` structures on adjunctions are compatible with opposites and pullbacks (#20363) Suppose that we use categories `C` and `D` equiped with a shifts by an additive monoid `A`, functors `F,F' : C ⥤ D`, a functor `G : D ⥤ C`, a natural transformation `τ : F ⟶ F'` and an adjunction `adj` between `F` and `G`. * For any map of additive monoids `φ : B →+ A`, we define type synonyms `PullbackShift.functor F φ` for `F`, `PullbackShift.natTrans τ φ` for `τ`, and `PullbackShift.adjunction adj φ` for `adj`. We then prove that a `CommShift` structure on `F` (resp. `τ`, resp. `adj`) induces a `CommShift` structure on `PullbackShift.functor F φ` (resp. `PullbackShift.natTrans τ φ`, resp. `PullbackShift.adjunction adj φ` ). * Similarly, we define type synonyms `OppositeShift.functor A F` for `F.op`, `OppositeShift.natTrans A τ` for `τ.op` and `OppositeShift.adjunction A adj` for `adj.op`, and prove that a `CommShift` structure on `F` (resp. `τ`, resp. `adj`) induces a `CommShift` structure on `OppositeShift.functor A F` (resp. `OppositeShift.natTrans A τ`, resp. `OppositeShift.adjunction A adj` ) for the naive shifts on the opposite categories. * The point of the second part is to reserve `F.op` etc to carry `CommShift` structures for the modified shift on the opposite categories used in the theory of (pre)triangulated categories. We illustrate this by simplifying the definition of the instance `commShiftOpInt` (a `CommShift ℤ` instance on `F.op` for the modified shifts) in the file `Triangulated.Opposite.Functor`. - [x] depends on: #20364 Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>
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…: `CommShift` structures on adjunctions are compatible with opposites and pullbacks (#20363) Suppose that we use categories `C` and `D` equiped with a shifts by an additive monoid `A`, functors `F,F' : C ⥤ D`, a functor `G : D ⥤ C`, a natural transformation `τ : F ⟶ F'` and an adjunction `adj` between `F` and `G`. * For any map of additive monoids `φ : B →+ A`, we define type synonyms `PullbackShift.functor F φ` for `F`, `PullbackShift.natTrans τ φ` for `τ`, and `PullbackShift.adjunction adj φ` for `adj`. We then prove that a `CommShift` structure on `F` (resp. `τ`, resp. `adj`) induces a `CommShift` structure on `PullbackShift.functor F φ` (resp. `PullbackShift.natTrans τ φ`, resp. `PullbackShift.adjunction adj φ` ). * Similarly, we define type synonyms `OppositeShift.functor A F` for `F.op`, `OppositeShift.natTrans A τ` for `τ.op` and `OppositeShift.adjunction A adj` for `adj.op`, and prove that a `CommShift` structure on `F` (resp. `τ`, resp. `adj`) induces a `CommShift` structure on `OppositeShift.functor A F` (resp. `OppositeShift.natTrans A τ`, resp. `OppositeShift.adjunction A adj` ) for the naive shifts on the opposite categories. * The point of the second part is to reserve `F.op` etc to carry `CommShift` structures for the modified shift on the opposite categories used in the theory of (pre)triangulated categories. We illustrate this by simplifying the definition of the instance `commShiftOpInt` (a `CommShift ℤ` instance on `F.op` for the modified shifts) in the file `Triangulated.Opposite.Functor`. - [x] depends on: #20364 Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>
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This PR improves some proofs about
NatTrans.CommShift(the commutation of a natural transformation to shifts). The fieldcomm'ofNatTrans.CommShifthad an unnecessary'in it, it is renamedshift_comm, and API lemmas are moved fromNatTrans.CommShiftto theNatTransnamespace (wherecommbecomesshift_commandcomm_appbecomesshift_app_comm).