Mathlib Map

Theorems · Definition · group theory

Con.ker

{M : Type u_1} →
  {N : Type u_2} →
    {F : Type u_4} → [inst : Mul M] → [inst_1 : Mul N] → [inst_2 : FunLike F M N] → [MulHomClass F M N] → F → Con M

The kernel of a multiplicative homomorphism as a congruence relation.

Defined in
Mathlib.GroupTheory.Congruence.Hom
Cited by
24 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
MulMulFunLikeMulHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Con.lift · cited by 12Con.liftCon.kerLift · cited by 4Con.kerLiftCon.hom_ext · cited by 3Con.hom_extCon.lift_range · cited by 2Con.lift_rangeCon.quotientKerEquivOfRightInverse · cited by 2Con.quotientKerEquivOfRig…Con.ker_rel · cited by 1Con.ker_relCon.lift_mk' · cited by 1Con.lift_mk'Con.lift_unique · cited by 1Con.lift_uniqueCon.mapOfSurjective · cited by 1Con.mapOfSurjectiveCon.mk'_ker · cited by 1Con.mk'_kerCon.kerLift_injective · cited by 0Con.kerLift_injectiveCon.kerLift_mk · cited by 0Con.kerLift_mkCon.kerLift_range_eq · cited by 0Con.kerLift_range_eqCon.ker_apply · cited by 0Con.ker_applyCon.ker_coeMulHom · cited by 0Con.ker_coeMulHomDFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeCon · cited by 152ConMulHomClass · cited by 73MulHomClassSetoid.ker · cited by 43Setoid.kerCon.kerCITED BYCITES

Cites5

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

Cited by31

Results whose statement or proof uses this declaration.