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Theorems · Theorem · group theory

MonoidHom.map_div

∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : DivisionMonoid β] (f : α →* β) (g h : α),
  f (g / h) = f g / f h

Group homomorphisms preserve division.

Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
6 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupDivisionMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Pi.mulSingle_div · cited by 1Pi.mulSingle_divCategoryTheory.GrpObj.comp_div · cited by 1GrpObj.comp_divCategoryTheory.GrpObj.div_comp · cited by 1GrpObj.div_compSet.mulIndicator_div · cited by 1Set.mulIndicator_divMonoidHom.map_div₂ · cited by 0MonoidHom.map_div₂AddChar.map_sub_eq_div · cited by 0AddChar.map_sub_eq_divDFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupMonoidHom · cited by 3629MonoidHomDivisionMonoid · cited by 201DivisionMonoidmap_div · cited by 20map_divMonoidHom.map_divCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.