Theorems · Theorem · ring theory

AlgEquiv.ofAlgHom_symm_apply

∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
  [inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (f : A₁ →ₐ[R] A₂) (g : A₂ →ₐ[R] A₁) (h₁ : f.comp g = AlgHom.id R A₂)
  (h₂ : g.comp f = AlgHom.id R A₁) (a : A₂), (AlgEquiv.ofAlgHom f g h₁ h₂).symm a = g a

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

12 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra