Theorems · Definition · category theory

CommBialgCat.isoEquivBialgEquiv

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

Bialgebra equivalences between Bialgebras are the same as isomorphisms in CommBialgCat.

Defined in

Mathlib.Algebra.Category.CommBialgCat

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingBialgebraCommRingBialgebra