Theorems · Theorem · group theory

QuotientGroup.injective_lift_iff

∀ {G : Type u_1} {M : Type u_4} [inst : Group G] [inst_1 : Monoid M] (N : Subgroup G) [nN : N.Normal] (φ : G →* M)
  (HN : N ≤ φ.ker), Function.Injective ⇑(QuotientGroup.lift N φ HN) ↔ N = φ.ker

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMonoidSubgroup.Normal