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Theorems · Theorem · group theory

AddCon.kerLift_injective

∀ {M : Type u_1} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass P] (f : M →+ P),
  Function.Injective ⇑(AddCon.kerLift f)

An AddMonoid homomorphism f induces an injective homomorphism on the quotient by f's kernel.

Defined in
Mathlib.GroupTheory.Congruence.Hom
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
AddZeroClassAddZeroClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

RingCon.kerLift_injective · cited by 1RingCon.kerLift_injectiveDFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddCon.Quotient · cited by 54AddCon.QuotientAddCon.ker · cited by 24AddCon.kerQuotient.inductionOn₂' · cited by 19Quotient.inductionOn₂'AddCon.eq · cited by 9AddCon.eqAddCon.kerLift · cited by 4AddCon.kerLiftAddCon.kerLift_injectiveCITED BYCITES

Cites8

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Cited by1

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