Theorems · Theorem · ring theory

MonoidAlgebra.bialgHom_ext_iff

∀ {R : Type u_1} {A : Type u_3} {B : Type u_4} {M : Type u_8} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Bialgebra R A] [inst_4 : Bialgebra R B] [inst_5 : Monoid M]
  {φ₁ φ₂ : MonoidAlgebra A M →ₐc[R] B},
  φ₁ = φ₂ ↔
    (∀ (m : M), φ₁ (MonoidAlgebra.single m 1) = φ₂ (MonoidAlgebra.single m 1)) ∧
      (↑φ₁).comp MonoidAlgebra.singleOneAlgHom = (↑φ₂).comp MonoidAlgebra.singleOneAlgHom

Defined in

Mathlib.RingTheory.Bialgebra.MonoidAlgebra

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringBialgebraBialgebraMonoid