Mathlib Map

Theorems · Theorem · group theory

AddCon.lift_coe

∀ {M : Type u_1} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass P] {c : AddCon M} {f : M →+ P}
  (H : c ≤ AddCon.ker f) (x : M), (c.lift f H) ↑x = f x

The diagram describing the universal property for quotients of AddMonoids commutes.

Defined in
Mathlib.GroupTheory.Congruence.Hom
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses Quot.sound
Assumes
AddZeroClassAddZeroClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PiTensorProduct.liftAux_tprod · cited by 2PiTensorProduct.liftAux_t…DFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddCon · cited by 138AddConAddCon.Quotient · cited by 54AddCon.QuotientAddCon.toQuotient · cited by 38AddCon.toQuotientAddCon.ker · cited by 24AddCon.kerAddCon.lift · cited by 14AddCon.liftAddCon.lift_coeCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.