Theorems · Definition · ring theory

HopfAlgebra.ofAlgHom

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring A] →
        [inst_2 : Bialgebra R A] →
          (antipode : A →ₐ[R] A) →
            (Algebra.TensorProduct.lift antipode (AlgHom.id R A) ⋯).comp (Bialgebra.comulAlgHom R A) =
                (Algebra.ofId R A).comp (Bialgebra.counitAlgHom R A) →
              (Algebra.TensorProduct.lift (AlgHom.id R A) antipode ⋯).comp (Bialgebra.comulAlgHom R A) =
                  (Algebra.ofId R A).comp (Bialgebra.counitAlgHom R A) →
                HopfAlgebra R A

Upgrade a commutative bialgebra to a Hopf algebra by specifying the antipode A →ₐ[R] A with appropriate conditions.

Defined in

Mathlib.RingTheory.HopfAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringBialgebra