feat(Condensed): closed symmetric monoidal structure on light condensed modules

[dagurtomas]

---

• depends on: feat(CategoryTheory): localization preserves braided structure #24485
• depends on: feat(CategoryTheory): transport symmetric monoidal structure along equivalence #24490
• depends on: chore(Condensed): introduce an abbrev for the equivalence of light condensed sets with a category of sheaves on a small site #24522

[github-actions]

PR summary 0665576140

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)	445
Mathlib.CategoryTheory.Monoidal.Braided.Transport (new file)	446
Mathlib.CategoryTheory.Localization.Monoidal.Braided (new file)	465
Mathlib.Condensed.Light.Small (new file)	1764
Mathlib.Condensed.Light.Monoidal (new file)	1919

---

Declarations diff

+ Transported.instBraidedCategory
+ Transported.instSymmetricCategory
+ associator_hom
+ associator_inv
+ braidedCategory
+ braidingNatIso
+ braidingNatIso_hom_app
+ braidingNatIso_hom_μ_left
+ braidingNatIso_hom_μ_right
+ braiding_naturality
+ curriedBraidingNatIso
+ equivSmall
+ instance (X Y : LightCondensed.{u} C) : Small.{max u v} (X ⟶ Y)
+ 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 : MonoidalCategory (LightCondMod.{u} R)
+ instance : MonoidalClosed (LightCondMod.{u} R)
+ instance : SymmetricCategory (LightCondMod.{u} R)
+ instance : SymmetricCategory (LocalizedMonoidal L W ε)
+ instance [(J.W (A := A)).IsMonoidal] [HasWeakSheafify J A] [BraidedCategory A] :
+ instance {C D : Type*} [Category C] [Category D]
+ map_hexagon_forward
+ map_hexagon_reverse
+ ofNatIso
+ symmetricCategory
+ symmetricCategoryOfFullyFaithful
+ β_hom_app
++++ instance (e : C ≌ D) [MonoidalCategory C] [BraidedCategory C] :
-++ 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
847	3	erw

Current commit 4338138860
Reference commit 0665576140

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): localization preserves braided structure #24485
• feat(CategoryTheory): transport symmetric monoidal structure along equivalence #24490
• chore(Condensed): introduce an abbrev for the equivalence of light condensed sets with a category of sheaves on a small site #24522
  By Dependent Issues (🤖). Happy coding!

[leanprover-community-bot-assistant]

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

[dagurtomas]

This PR has been migrated to a fork-based workflow: #25797