Theorems · Definition · group theory

MulHom.coprod

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

Coproduct of two MulHoms with the same codomain: f.coprod g (p : M × N) = f p.1 * g p.2. (Commutative codomain; for the general case, see MulHom.noncommCoprod)

Defined in

Mathlib.Algebra.Group.Prod

Cited by

2 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext

Assumes

MulMulCommSemigroup