Theorems · Definition · group theory

QuotientGroup.lift

{G : Type u_1} →
  {M : Type u_4} →
    [inst : Group G] → [inst_1 : Monoid M] → (N : Subgroup G) → [nN : N.Normal] → (φ : G →* M) → N ≤ φ.ker → G ⧸ N →* M

A group homomorphism φ : G →* M with N ⊆ ker(φ) descends (i.e. lifts) to a group homomorphism G/N →* M.

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

8 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMonoidSubgroup.Normal