[Merged by Bors] - feat: the category of Hopf algebras

[101damnations]

The category of Hopf algebras over a commutative ring. Mimics Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.

---

• depends on: [Merged by Bors] - feat: coalgebra homomorphisms #11961
• depends on: [Merged by Bors] - feat: bialgebra homomorphisms #11962
• depends on: [Merged by Bors] - feat: coalgebra isomorphisms #11970
• depends on: [Merged by Bors] - feat: bialgebra isomorphisms #11971
• depends on: [Merged by Bors] - feat: category of coalgebras #11972
• depends on: [Merged by Bors] - feat: category of bialgebras  #11973

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• [Merged by Bors] - feat: coalgebra homomorphisms #11961
• [Merged by Bors] - feat: bialgebra homomorphisms #11962
• [Merged by Bors] - feat: coalgebra isomorphisms #11970
• [Merged by Bors] - feat: bialgebra isomorphisms #11971
• [Merged by Bors] - feat: category of coalgebras #11972
• [Merged by Bors] - feat: category of bialgebras  #11973
  By Dependent Issues (🤖). Happy coding!

[github-actions]

PR summary b456518308

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Category.HopfAlgebraCat.Basic	1228

---

Declarations diff

+ Hom
+ Hom.toBialgHom_injective
+ HopfAlgebraCat
+ HopfAlgebraCat.forget_reflects_isos
+ category
+ concreteCategory
+ forget₂_bialgebra_map
+ forget₂_bialgebra_obj
+ hasForgetToBialgebra
+ hom_ext
+ instance : CoeSort (HopfAlgebraCat.{v} R) (Type v)
+ of
+ of_comul
+ of_counit
+ toBialgHom_comp
+ toBialgHom_id
+ toHopfAlgEquiv
+ toHopfAlgEquiv_refl
+ toHopfAlgEquiv_symm
+ toHopfAlgEquiv_toBialgHom
+ toHopfAlgEquiv_trans
+ toHopfAlgebraCatIso
+ toHopfAlgebraCatIso_refl
+ toHopfAlgebraCatIso_symm
+ toHopfAlgebraCatIso_trans

You can run this locally as follows

## summary with just the declaration names:
./scripts/no_lost_declarations.sh short <optional_commit>

## more verbose report:
./scripts/no_lost_declarations.sh <optional_commit>

[kim-em]

bors merge

[mathlib-bors]

This PR was included in a batch that was canceled, it will be automatically retried

[mathlib-bors]

Pull request successfully merged into master.

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