Theorems · Definition · ring theory

BialgEquiv.ofBijective

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Bialgebra R A] → [inst_4 : Bialgebra R B] → (f : A →ₐc[R] B) → Function.Bijective ⇑f → A ≃ₐc[R] B

Promotes a bijective bialgebra homomorphism to a bialgebra equivalence.

Defined in

Mathlib.RingTheory.Bialgebra.Equiv

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringBialgebraBialgebra