Theorems · Definition · group theory

MonoidHom.mker

{M : Type u_1} →
  {N : Type u_2} →
    [inst : MulOneClass M] →
      [inst_1 : MulOneClass N] →
        {F : Type u_4} → [inst_2 : FunLike F M N] → [mc : MonoidHomClass F M N] → F → Submonoid M

The multiplicative kernel of a MonoidHom is the Submonoid of elements x : G such that f x = 1.

Defined in

Mathlib.Algebra.Group.Submonoid.Operations

Cited by

24 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

MulOneClassMulOneClassFunLikeMonoidHomClass