Theorems · Definition · ring theory

StarAlgEquiv.ofNonUnitalStarAlgHom

{R : Type u_1} →
  {A₁ : Type u_2} →
    {A₂ : Type u_3} →
      [inst : Monoid R] →
        [inst_1 : NonUnitalNonAssocSemiring A₁] →
          [inst_2 : DistribMulAction R A₁] →
            [inst_3 : Star A₁] →
              [inst_4 : NonUnitalNonAssocSemiring A₂] →
                [inst_5 : DistribMulAction R A₂] →
                  [inst_6 : Star A₂] →
                    (f : A₁ →⋆ₙₐ[R] A₂) →
                      (g : A₂ →⋆ₙₐ[R] A₁) →
                        g.comp f = NonUnitalStarAlgHom.id R A₁ → f.comp g = NonUnitalStarAlgHom.id R A₂ → A₁ ≃⋆ₐ[R] A₂

Construct a star algebra equivalence from a pair of non-unital star algebra homomorphisms.

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

5 results in Mathlib

Foundations

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

Assumes

MonoidNonUnitalNonAssocSemiringDistribMulActionStarNonUnitalNonAssocSemiringDistribMulActionStar