feat(CategoryTheory/Sums/Basic): compatibility of Sum.functorEquiv and Sum.Swap.equivalence

[robin-carlier]

Show that Sum.functorEquiv transforms Sum.Swap.Equivalence into Prod.braiding.

---

• depends on: feat(CategoryTheory/Equivalence): equivalences with isomorphic functors have isomorphic inverses #22287
• depends on: feat(CategoryTheory/Sums/Basic): functors out of Sum #22278

[github-actions]

PR summary 3c11504184

Import changes exceeding 2%

%	File
+2.13%	Mathlib.CategoryTheory.Sums.Basic

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Sums.Basic	282	288	+6 (+2.13%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Sums.Associator Mathlib.CategoryTheory.Sums.Basic	6

---

Declarations diff

+ equivalenceFunctorEquivFunctorIso
+ equivalenceFunctorEquivInverseIso
+ functorEquiv
+ functorEquivFunctorCompFstIso
+ functorEquivFunctorCompSndIso
+ functorEquivInverseCompWhiskeringLeftInLIso
+ functorEquivInverseCompWhiskeringLeftInRIso
+ isoFunctorOfIsoInverse
+ isoFunctorOfIsoInverse_isoInverseOfIsoFunctor
+ isoInverseOfIsoFunctor
+ isoInverseOfIsoFunctor_isoFunctorOfIsoInverse
+ sum'_app_inl
+ sum'_app_inr
+-+ sum'

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.

---

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:

• feat(CategoryTheory/Equivalence): equivalences with isomorphic functors have isomorphic inverses #22287
• feat(CategoryTheory/Sums/Basic): functors out of Sum #22278
  By Dependent Issues (🤖). Happy coding!