Theorems · Theorem · ring theory

BialgHom.ext

∀ {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 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : CoalgebraStruct R A] [inst_6 : CoalgebraStruct R B]
  {φ₁ φ₂ : A →ₐc[R] B}, (∀ (x : A), φ₁ x = φ₂ x) → φ₁ = φ₂

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

9 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraCoalgebraStructCoalgebraStruct