…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>

* origin/master: (189 commits)
  chore(Algebra): make more names consistent (#20449)
  feat: Polynomial FLT (#18882)
  feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty (#20457)
  fix: linkfix in 100.yaml (#20517)
  feat(1000): fill in more entries (#20470)
  feat(Combinatorics/SimpleGraph/Walk): add `penultimate` and `snd` (#16769)
  feat(ContinuousMultilinearMap): add lemmas about `.prod` (#20462)
  feat(RingTheory): classification of etale algebras over fields (#20324)
  fix: Allow multiple builds on staging branch (#20515)
  feat(CategoryTheory/Shift/Adjunction): properties of `Adjunction.CommShift` (#20337)
  chore(Data/Multiset/Basic): move the `sub`, `union`, `inter` sections lower (#19863)
  chore(Topology/UniformSpace/Completion): make coe' argument implicit (#20514)
  refactor(Algebra/Category/Grp/Colimits): change the construction of colimits in `AddCommGrp` (#20474)
  feat(Topology/Algebra/InfiniteSum/NatInt): Add pnat lems (#16544)
  chore(RingTheory/Finiteness): rename Module.Finite.out (#20506)
  refactor(CategoryTheory/Limits/Preserves/Ulift): simplify the proof that the universe lifting functor for types preserves all colimits (#20508)
  feat(CategoryTheory): products in the category of Ind-objects (#20507)
  chore: remove >9 month old deprecations (#20505)
  chore(FieldTheory/Galois): small cleanup (#20217)
  chore(LinearIndependent): generalize to semirings (#20480)
  chore(NumberTheory/NumberField/AdeleRing): refactor adele rings (#20500)
  chore: replace `aesop` with `simp` where possible (#20483)
  chore(1000): remove nonexistent fields (#20493)
  chore(CategoryTheory/Adjunction.Basic, CategoryTheory/Equivalence): change definition of `Adjunction.comp` and `Equivalence.trans` (#20490)
  feat(Asymptotics): add `Asymptotics.*.*Prod` lemmas (#20458)
  feat: a conditional kernel is almost everywhere a probability measure (#20430)
  feat: if `f` is a measurable group hom, then every point has a neighborhood `s` such that `f '' s` is bounded (#20304)
  feat: `Ico`, `Ioc`, and `Ioo` are not closed or compact (#20479)
  chore: drop redundant hypothesis in `Module.Dual.eq_of_preReflection_mapsTo` (#20492)
  feat(FaaDiBruno): derive `DecidableEq` (#20482)
  chore(SetTheory/Ordinal/Basic): `{x // x < y}` → `Iio y` (#20413)
  chore: generalize `FormalMultilinearSeries.ofScalars_norm` to `Seminormed` (#20351)
  chore(MvPolynomial/Localization): golf using TensorProduct (#20309)
  chore(Combinatorics/Enumerative/Partition): auto-derive DecidableEq (#20277)
  chore(CategoryTheory): make relevant parameters explicit in `Arrow.homMk`. (#20259)
  feat: add `IsStarNormal (↑x⁻¹ : R)` instance for `x : Rˣ` (#20091)
  fix: Stop cancelling builds of master (#20435)
  chore: update Mathlib dependencies 2025-01-05 (#20485)
  feat(SetTheory/Cardinal/Arithmetic): miscellaneous cardinality lemmas (#18933)
  chore: bump toolchain to v4.16.0-rc1, and merge bump/v4.16.0 (#20464)
  chore: bot validates lean-toolchain on bump/v4.X.0 branches (#20478)
  feat: shorthand lemmas for the L1 norm (#20383)
  chore: remove unnecessary adaptation notes (#20467)
  chore(Algebra/Category/MonCat/Colimits): remove smallness condition (#20473)
  chore(SetTheory/Ordinal/Arithmetic): `IsLeftCancelAdd Ordinal` (#19888)
  feat(Algebra): more on `OrthogonalIdempotents` (#18195)
  feat(Radical): `(radical a).natDegree ≤ a.natDegree` (#20468)
  feat(Polynomial): `(a^n)' = 0` iff `a' = 0` when `n` doesn't divide the characteristic (#20190)
  feat(Algebra/Lie): add Lie's theorem (#13480)
  chore(RingTheory/Generators): make algebra instance a def (#14265)
  ...

…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>