Theorems · Definition · group theory

MulHom.prod

{M : Type u_3} →
  {N : Type u_4} →
    {P : Type u_5} → [inst : Mul M] → [inst_1 : Mul N] → [inst_2 : Mul P] → (M →ₙ* N) → (M →ₙ* P) → M →ₙ* N × P

Combine two MonoidHoms f : M →ₙ* N, g : M →ₙ* P into f.prod g : M →ₙ* (N × P) given by (f.prod g) x = (f x, g x).

Defined in

Mathlib.Algebra.Group.Prod

Cited by

7 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

MulMulMul