Theorems · Theorem · group theory

map_div

∀ {G : Type u_7} {H : Type u_8} {F : Type u_9} [inst : FunLike F G H] [inst_1 : Group G] [inst_2 : DivisionMonoid H]
  [MonoidHomClass F G H] (f : F) (a b : G), f (a / b) = f a / f b

Group homomorphisms preserve division. See note [hom simp lemma priority]

Defined in

Mathlib.Algebra.Group.Hom.Defs

Cited by

20 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLikeGroupDivisionMonoidMonoidHomClass