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Theorems · Definition · category theory

BialgCat.ofHom

{R : Type u} →
  [inst : CommRing R] →
    {X Y : Type v} →
      [inst_1 : Ring X] →
        [inst_2 : Ring Y] →
          [inst_3 : Bialgebra R X] → [inst_4 : Bialgebra R Y] → (X →ₐc[R] Y) → (BialgCat.of R X ⟶ BialgCat.of R Y)

Typecheck a BialgHom as a morphism in BialgCat R.

Defined in
Mathlib.Algebra.Category.BialgCat.Basic
Cited by
6 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Quot.sound
Assumes
CommRingRingRingBialgebraBialgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

BialgEquiv.toBialgIso · cited by 8BialgEquiv.toBialgIsoBialgEquiv.toBialgIso_hom · cited by 0BialgEquiv.toBialgIso_homBialgEquiv.toBialgIso_inv · cited by 0BialgEquiv.toBialgIso_invBialgCat.tensorHom_def · cited by 0BialgCat.tensorHom_defBialgCat.whiskerLeft_def · cited by 0BialgCat.whiskerLeft_defBialgCat.whiskerRight_def · cited by 0BialgCat.whiskerRight_defHopfAlgCat.forget₂_bialgebra_map · cited by 0HopfAlgCat.forget₂_bialge…Quiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingRing · cited by 7463RingBialgHom · cited by 190BialgHomBialgebra · cited by 160BialgebraBialgCat · cited by 40BialgCatCategoryTheory.ConcreteCategory.ofHom · cited by 18ConcreteCategory.ofHomBialgCat.of · cited by 17BialgCat.ofBialgCat.ofHomCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.