feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated

[smorel394]

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]

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[github-actions]

PR summary 6372b3aa48

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

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Declarations diff

+ IsTriangulated
+ isTriangulated_rightAdjoint
+ mk'
+ 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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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• 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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

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