Theorems · Theorem · ring theory

Unitization.algHom_ext

∀ {S : Type u_1} {R : Type u_2} {A : Type u_3} [inst : CommSemiring S] [inst_1 : CommSemiring R]
  [inst_2 : NonUnitalSemiring A] [inst_3 : Module R A] [inst_4 : SMulCommClass R A A] [inst_5 : IsScalarTower R A A]
  {B : Type u_4} [inst_6 : Semiring B] [inst_7 : Algebra S B] [inst_8 : Algebra S R] [inst_9 : DistribMulAction S A]
  [inst_10 : IsScalarTower S R A] {F : Type u_6} [inst_11 : FunLike F (Unitization R A) B]
  [AlgHomClass F S (Unitization R A) B] {φ ψ : F},
  (∀ (a : A), φ ↑a = ψ ↑a) →
    (∀ (r : R), φ ((algebraMap R (Unitization R A)) r) = ψ ((algebraMap R (Unitization R A)) r)) → φ = ψ

Defined in

Mathlib.Algebra.Algebra.Unitization

Cited by

1 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringNonUnitalSemiringModuleSMulCommClassIsScalarTowerSemiringAlgebraAlgebraDistribMulActionIsScalarTowerFunLikeAlgHomClass