Theorems · Theorem · group theory

MonoidHom.commute_noncommPiCoprod

∀ {M : Type u_1} [inst : Monoid M] {ι : Type u_2} [inst_1 : Fintype ι] {N : ι → Type u_3}
  [inst_2 : (i : ι) → Monoid (N i)] (ϕ : (i : ι) → N i →* M)
  {hcomm : Pairwise fun i j => ∀ (x : N i) (y : N j), Commute ((ϕ i) x) ((ϕ j) y)} {m : M},
  (∀ (i : ι) (x : N i), Commute m ((ϕ i) x)) → ∀ (h : (i : ι) → N i), Commute m ((MonoidHom.noncommPiCoprod ϕ hcomm) h)

Defined in

Mathlib.GroupTheory.NoncommPiCoprod

Cited by

0 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidFintypeMonoid