Theorems · Definition · group theory
Algebra.GrothendieckGroup.lift
{M : Type u_1} →
{G : Type u_2} → [inst : CommMonoid M] → [inst_1 : CommGroup G] → (M →* G) ≃ (Algebra.GrothendieckGroup M →* G)A monoid homomorphism from a monoid M to a group G lifts to a group homomorphism from the
Grothendieck group of M to G.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Equivstatement · cited by 8,337
- MonoidHomstatement and proof · cited by 3,629
- Submonoidstatement · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- CommGroupstatement and proof · cited by 990
- MonoidHom.compproof · cited by 469
- Submonoid.LocalizationMap.liftproof · cited by 26
- Localization.monoidOfproof · cited by 17
- Algebra.GrothendieckGroupstatement and proof · cited by 3
- Algebra.GrothendieckGroup.ofproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.GrothendieckGroup.lift_applystatement · cited by 0
- Algebra.GrothendieckGroup.lift_symm_applystatement and proof · cited by 0