feat(CategoryTheory): localization preserves braided structure

[dagurtomas]

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[github-actions]

PR summary b5fd4fb167

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Localization.Monoidal Mathlib.CategoryTheory.Sites.Monoidal	1
Mathlib.CategoryTheory.Localization.Monoidal.Basic (new file)	444
Mathlib.CategoryTheory.Localization.Monoidal.Braided (new file)	464

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Declarations diff

+ associator_hom
+ associator_inv
+ braidedCategory
+ braidingNatIso
+ braidingNatIso_hom_app
+ braidingNatIso_hom_μ_left
+ braidingNatIso_hom_μ_right
+ braiding_naturality
+ curriedBraidingNatIso
+ instance : (toMonoidalCategory L W ε).Braided
+ instance : BraidedCategory (LocalizedMonoidal L W ε)
+ instance : Lifting₂ L' L' W W ((curriedTensor C).flip ⋙ (whiskeringRight C C
+ instance : SymmetricCategory (LocalizedMonoidal L W ε)
+ instance [(J.W (A := A)).IsMonoidal] [HasWeakSheafify J A] [BraidedCategory A] :
+ map_hexagon_forward
+ map_hexagon_reverse
+ symmetricCategory
+ β_hom_app
-++ instance : (L').IsLocalization W := inferInstanceAs (L.IsLocalization W)

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.

---

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

Current number	Change	Type
903	3	erw

Current commit b5fd4fb167
Reference commit 58bea69247

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).

[leanprover-community-bot-assistant]

This pull request has conflicts, please merge master and resolve them.

[joelriou]

Could you add the relevant deprecated_module?

[dagurtomas]

I'm not familiar with deprecated module, I hope I did it correctly.

[dagurtomas]

This PR has been migrated to a fork-based workflow: #25794