Theorems · Theorem · ring theory

BialgHom.ofAlgHom_apply

∀ {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)
  (counit_comp : (Bialgebra.counitAlgHom R B).comp f = Bialgebra.counitAlgHom R A)
  (map_comp_comul :
    (Algebra.TensorProduct.map f f).comp (Bialgebra.comulAlgHom R A) = (Bialgebra.comulAlgHom R B).comp f)
  (a : A), (BialgHom.ofAlgHom f counit_comp map_comp_comul) a = f a

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringSemiringBialgebraBialgebra