Theorems · Definition · ring theory

AlgEquivClass.toAlgEquiv

{F : Type u_1} →
  {R : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Semiring B] →
              [inst_3 : Algebra R A] →
                [inst_4 : Algebra R B] → [inst_5 : EquivLike F A B] → [AlgEquivClass F R A B] → F → A ≃ₐ[R] B

Turn an element of a type F satisfying AlgEquivClass F R A B into an actual AlgEquiv. This is declared as the default coercion from F to A ≃ₐ[R] B.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

12 results in Mathlib

Foundations

Depth 17 from the axioms · uses Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraEquivLikeAlgEquivClass