Theorems · Definition · ring theory

BialgHom.ofAlgHom

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Bialgebra R A] →
              [inst_4 : Bialgebra R B] →
                (f : A →ₐ[R] B) →
                  (Bialgebra.counitAlgHom R B).comp f = Bialgebra.counitAlgHom R A →
                    (Algebra.TensorProduct.map f f).comp (Bialgebra.comulAlgHom R A) =
                        (Bialgebra.comulAlgHom R B).comp f →
                      A →ₐc[R] B

Construct a bialgebra hom from an algebra hom respecting counit and comultiplication.

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

9 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringBialgebraBialgebra