Theorems · Theorem · group theory

AddCon.lift_surjective_of_surjective

∀ {M : Type u_1} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass P] {c : AddCon M} {f : M →+ P}
  (h : c ≤ AddCon.ker f), Function.Surjective ⇑f → Function.Surjective ⇑(c.lift f h)

Surjective AddMonoid homomorphisms constant on an additive congruence relation c's equivalence classes induce a surjective homomorphism on c's quotient.

Defined in

Mathlib.GroupTheory.Congruence.Hom

Cited by

1 results in Mathlib

Foundations

Depth 17 from the axioms · uses Quot.sound

Assumes

AddZeroClassAddZeroClass