Theorems · Definition · ring theory

StarAlgHom.prodEquiv

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {C : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : Star A] →
                [inst_4 : Semiring B] →
                  [inst_5 : Algebra R B] →
                    [inst_6 : Star B] →
                      [inst_7 : Semiring C] →
                        [inst_8 : Algebra R C] → [inst_9 : Star C] → (A →⋆ₐ[R] B) × (A →⋆ₐ[R] C) ≃ (A →⋆ₐ[R] B × C)

Taking the product of two maps with the same domain is equivalent to taking the product of their codomains.

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraStarSemiringAlgebraStarSemiringAlgebraStar