Theorems · Definition · group theory

AddMonoidHom.coprod

{M : Type u_3} →
  {N : Type u_4} →
    {P : Type u_5} →
      [inst : AddZeroClass M] →
        [inst_1 : AddZeroClass N] → [inst_2 : AddCommMonoid P] → (M →+ P) → (N →+ P) → M × N →+ P

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

Defined in

Mathlib.Algebra.Group.Prod

Cited by

7 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

AddZeroClassAddZeroClassAddCommMonoid