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

[smorel394]

If a functor G : D ⥤ C between pretriangulated categories is triangulated, and if we have an adjunction F ⊣ G (that commutes with the shifts), then F is also a triangulated functor.

We prove this from the symmetric statement (F triangulated implies G triangulated) using opposite categories.

• depends on: feat(CategoryTheory/Shift/Opposite and CategoryTheory/Shift/Pullback): CommShift structures on adjunctions are compatible with opposites and pullbacks #20363

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[github-actions]

PR summary 0fa5895c52

Import changes exceeding 2%

%	File
+5.97%	Mathlib.CategoryTheory.Triangulated.Adjunction

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Triangulated.Adjunction	1105	1171	+66 (+5.97%)
Mathlib.CategoryTheory.Shift.Pullback	681	685	+4 (+0.59%)
Mathlib.CategoryTheory.Shift.Opposite	806	810	+4 (+0.50%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences	2
Mathlib.CategoryTheory.Triangulated.Yoneda	3
7 files Mathlib.CategoryTheory.Triangulated.Opposite.Functor Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated Mathlib.CategoryTheory.Shift.ShiftedHomOpposite Mathlib.CategoryTheory.Triangulated.Opposite.Triangle Mathlib.CategoryTheory.Shift.Opposite Mathlib.CategoryTheory.Triangulated.Opposite.Basic Mathlib.CategoryTheory.Shift.Pullback	4
Mathlib.CategoryTheory.Triangulated.Adjunction	66

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Declarations diff

+ PullbackShift.adjunction
+ PullbackShift.functor
+ PullbackShift.natIsoComp
+ PullbackShift.natIsoId
+ PullbackShift.natTrans
+ instance : NatTrans.CommShift (PullbackShift.natIsoComp φ F G).hom A
+ instance : NatTrans.CommShift (PullbackShift.natIsoId C φ).hom A
+ isTriangulated_leftAdjoint
+ mk''
++ commShift_op
+++ on
-+++ commShiftPullback

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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Decrease in tech debt: (relative, absolute) = (3.00, 0.00)

Current number	Change	Type
1453	-3	erw

Current commit 0fa5895c52
Reference commit 1a9143ba4b

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:

• feat(CategoryTheory/Shift/Opposite and CategoryTheory/Shift/Pullback): CommShift structures on adjunctions are compatible with opposites and pullbacks #20363
  By Dependent Issues (🤖). Happy coding!