Theorems · Definition · group theory
Submonoid.LocalizationMap.AwayMap
{M : Type u_1} → [CommMonoid M] → M → (N' : Type u_4) → [CommMonoid N'] → Type (max u_1 u_4)Given x : M, the type of CommMonoid homomorphisms f : M →* N such that N
is isomorphic to the Localization of M at the Submonoid generated by x.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.powersproof · cited by 408
- Submonoid.LocalizationMapproof · cited by 147
Cited by7
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.AwayMap.liftstatement and proof · cited by 2
- Localization.Away.monoidOfstatement · cited by 1
- Submonoid.LocalizationMap.AwayMap.invSelfstatement and proof · cited by 0
- Submonoid.LocalizationMap.AwayMap.lift_compstatement and proof · cited by 0
- Submonoid.LocalizationMap.AwayMap.lift_eqstatement and proof · cited by 0
- Localization.Away.mulEquivOfQuotientstatement and proof · cited by 0
- Submonoid.LocalizationMap.awayToAwayRightstatement and proof · cited by 0