Theorems · Theorem · ring theory

AlgHom.prod_comp

∀ {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]
  {C' : Type u_5} [inst_7 : Semiring C'] [inst_8 : Algebra R C'] (f : A →ₐ[R] B) (g : B →ₐ[R] C) (g' : B →ₐ[R] C'),
  (g.prod g').comp f = (g.comp f).prod (g'.comp f)

Defined in

Mathlib.Algebra.Algebra.Prod

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraSemiringAlgebraSemiringAlgebra