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Theorems · Theorem · group theory

Con.ker_rel

∀ {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]
  [inst_3 : MulHomClass F M N] (f : F) {x y : M}, (Con.ker f) x y ↔ f x = f y

The definition of the congruence relation defined by a monoid homomorphism's kernel.

Defined in
Mathlib.GroupTheory.Congruence.Hom
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
MulMulFunLikeMulHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

QuotientGroup.con_ker_eq_conKer · cited by 0QuotientGroup.con_ker_eq_…DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeCon · cited by 152ConMulHomClass · cited by 73MulHomClassCon.ker · cited by 24Con.kerCon.ker_relCITED BYCITES

Cites5

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Cited by1

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