Theorems · Definition · nonassociative algebras

NonUnitalAlgHom.prodEquiv

{R : Type u} →
  [inst : Monoid R] →
    {A : Type v} →
      {B : Type w} →
        {C : Type w₁} →
          [inst_1 : NonUnitalNonAssocSemiring A] →
            [inst_2 : DistribMulAction R A] →
              [inst_3 : NonUnitalNonAssocSemiring B] →
                [inst_4 : NonUnitalNonAssocSemiring C] →
                  [inst_5 : DistribMulAction R B] →
                    [inst_6 : DistribMulAction R C] → (A →ₙₐ[R] B) × (A →ₙₐ[R] C) ≃ (A →ₙₐ[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.NonUnitalHom

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

MonoidNonUnitalNonAssocSemiringDistribMulActionNonUnitalNonAssocSemiringNonUnitalNonAssocSemiringDistribMulActionDistribMulAction