Theorems · Definition · ring theory

AlgHom.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 : Semiring B] →
                [inst_4 : Algebra R B] →
                  [inst_5 : Semiring C] → [inst_6 : Algebra R 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.Algebra.Prod

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraSemiringAlgebra