Theorems · Theorem · group theory

Submonoid.LocalizationMap.comp_eq_of_eq

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

Given CommMonoids M, P, Localization maps f : M →* N, k : P →* Q for Submonoids 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

CommMonoidCommMonoidCommMonoidCommMonoid