Theorems · Theorem · group theory

AddSubmonoid.LocalizationMap.comp_eq_of_eq

∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N] {P : Type u_3}
  [inst_2 : AddCommMonoid P] (f : S.LocalizationMap N) {g : M →+ P} {T : AddSubmonoid P} {Q : Type u_4}
  [inst_3 : AddCommMonoid Q],
  (∀ (y : ↥S), g ↑y ∈ T) → ∀ (k : T.LocalizationMap Q) {x y : M}, f x = f y → k (g x) = k (g y)

Given AddCommMonoids M, P, Localization maps f : M →+ N, k : P →+ Q for AddSubmonoids S, T respectively, and g : M →+ P such that g(S) ⊆ T, f x = f y implies k (g x) = k (g y).

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

1 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoid