Theorems · Theorem · group theory

QuotientAddGroup.injective_lift_iff

∀ {G : Type u_1} {M : Type u_4} [inst : AddGroup G] [inst_1 : AddMonoid M] (N : AddSubgroup G) [nN : N.Normal]
  (φ : G →+ M) (HN : N ≤ φ.ker), Function.Injective ⇑(QuotientAddGroup.lift N φ HN) ↔ N = φ.ker

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

AddGroupAddMonoidAddSubgroup.Normal