Theorems · Definition · ring theory

HopfAlgebra.ofConvInverse

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        [inst_2 : Bialgebra R A] →
          (antipode : A →ₗ[R] A) →
            WithConv.toConv antipode * WithConv.toConv LinearMap.id = 1 →
              WithConv.toConv LinearMap.id * WithConv.toConv antipode = 1 → HopfAlgebra R A

Upgrade a bialgebra to a Hopf algebra by specifying a convolution inverse of the identity.

Defined in

Mathlib.RingTheory.HopfAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringBialgebra