Mathlib Map

Theorems · Definition · group theory

Con.kerLift

{M : Type u_1} →
  {P : Type u_3} → [inst : MulOneClass M] → [inst_1 : MulOneClass P] → (f : M →* P) → (Con.ker f).Quotient →* P

The homomorphism induced on the quotient of a monoid by the kernel of a monoid homomorphism.

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

Around this declaration

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

Con.quotientKerEquivOfRightInverse · cited by 2Con.quotientKerEquivOfRig…Con.quotientKerEquivOfRightInverse_apply · cited by 0Con.quotientKerEquivOfRig…Con.kerLift_injective · cited by 0Con.kerLift_injectiveCon.kerLift_mk · cited by 0Con.kerLift_mkCon.kerLift_range_eq · cited by 0Con.kerLift_range_eqCon.quotientKerEquivRange · cited by 0Con.quotientKerEquivRangeMonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassCon.Quotient · cited by 48Con.QuotientCon.ker · cited by 24Con.kerCon.lift · cited by 12Con.liftCon.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.