Theorems · Theorem · group theory

Submonoid.LocalizationMap.map_comp_map

∀ {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} (hy : ∀ (y : ↥S), g ↑y ∈ T)
  {Q : Type u_4} [inst_3 : CommMonoid Q] {k : T.LocalizationMap Q} {A : Type u_5} [inst_4 : CommMonoid A]
  {U : Submonoid A} {R : Type u_6} [inst_5 : CommMonoid R] (j : U.LocalizationMap R) {l : P →* A}
  (hl : ∀ (w : ↥T), l ↑w ∈ U), (k.map hl j).comp (f.map hy k) = f.map ⋯ j

If CommMonoid homs g : M →* P, l : P →* A induce maps of localizations, the composition of the induced maps equals the map of localizations induced by l ∘ g.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoidCommMonoidCommMonoidCommMonoid