Theorems · Definition · group theory
Localization.mk
{M : Type u_1} → [inst : CommMonoid M] → {S : Submonoid M} → M → ↥S → Localization SGiven a CommMonoid M and submonoid S, mk sends x : M, y ∈ S to the equivalence
class of (x, y) in the localization of M at S.
- Cited by
- 110 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 176 definitions · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Localizationstatement · cited by 270
- OreLocalization.oreDivproof · cited by 72
Cited by120
Results whose statement or proof uses this declaration.
- Localization.mk_eq_mk'statement · cited by 25
- Localization.monoidOfproof · cited by 17
- HomogeneousLocalization.val_mkstatement · cited by 14
- Localization.mk_mulstatement · cited by 12
- Localization.mk_eq_mk_iffstatement · cited by 9
- HomogeneousLocalization.val_mulproof · cited by 9
- Localization.induction_onstatement and proof · cited by 9
- HomogeneousLocalization.NumDenSameDeg.embeddingproof · cited by 9
- Localization.mk_zerostatement · cited by 8
- RatFunc.mapproof · cited by 8
- Localization.mk_powstatement · cited by 6
- Localization.mk_eq_monoidOf_mk'statement · cited by 5