Theorems · Theorem · group theory

Con.lift_range

∀ {M : Type u_1} {P : Type u_3} [inst : MulOneClass M] [inst_1 : MulOneClass P] {c : Con M} {f : M →* P}
  (H : c ≤ Con.ker f), MonoidHom.mrange (c.lift f H) = MonoidHom.mrange f

Given a congruence relation c on a monoid and a homomorphism f constant on c's equivalence classes, f has the same image as the homomorphism that f induces on the quotient.

Defined in

Mathlib.GroupTheory.Congruence.Basic

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MulOneClassMulOneClass