Mathlib Map

Theorems · Definition · group theory

AddCon.kerLift

{M : Type u_1} →
  {P : Type u_3} → [inst : AddZeroClass M] → [inst_1 : AddZeroClass P] → (f : M →+ P) → (AddCon.ker f).Quotient →+ P

The homomorphism induced on the quotient of an AddMonoid by the kernel of an AddMonoid homomorphism.

Defined in
Mathlib.GroupTheory.Congruence.Hom
Cited by
4 results in Mathlib
Foundations
Depth 16 from the axioms · uses Quot.sound
Assumes
AddZeroClassAddZeroClass
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Around this declaration

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

AddCon.quotientKerEquivOfRightInverse · cited by 2AddCon.quotientKerEquivOf…AddCon.kerLift_injective · cited by 1AddCon.kerLift_injectiveAddCon.quotientKerEquivOfRightInverse_apply · cited by 0AddCon.quotientKerEquivOf…AddCon.quotientKerEquivRange · cited by 0AddCon.quotientKerEquivRa…AddCon.kerLift_mk · cited by 0AddCon.kerLift_mkAddCon.kerLift_range_eq · cited by 0AddCon.kerLift_range_eqAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddCon.Quotient · cited by 54AddCon.QuotientAddCon.ker · cited by 24AddCon.kerAddCon.lift · cited by 14AddCon.liftAddCon.kerLiftCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.