Mathlib Map

Theorems · Definition · group theory

QuotientAddGroup.homQuotientZSMulOfHom

{A B : Type u} →
  [inst : AddCommGroup A] →
    [inst_1 : AddCommGroup B] → (A →+ B) → (n : ℤ) → A ⧸ (zsmulAddGroupHom n).range →+ B ⧸ (zsmulAddGroupHom n).range

The map of quotients by multiples of an integer induced by an additive group homomorphism.

Defined in
Mathlib.GroupTheory.QuotientGroup.Basic
Cited by
3 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupAddCommGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

QuotientAddGroup.equivQuotientZSMulOfEquiv · cited by 3QuotientAddGroup.equivQuo…QuotientAddGroup.homQuotientZSMulOfHom_comp · cited by 0QuotientAddGroup.homQuoti…QuotientAddGroup.homQuotientZSMulOfHom_comp_of_rightInverse · cited by 0QuotientAddGroup.homQuoti…QuotientAddGroup.homQuotientZSMulOfHom_id · cited by 0QuotientAddGroup.homQuoti…AddCommGroup · cited by 12871AddCommGroupAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomHasQuotient.Quotient · cited by 2301HasQuotient.QuotientAddMonoidHom.comp · cited by 339AddMonoidHom.compAddMonoidHom.range · cited by 142AddMonoidHom.rangeQuotientAddGroup.mk' · cited by 60QuotientAddGroup.mk'QuotientAddGroup.lift · cited by 15QuotientAddGroup.liftzsmulAddGroupHom · cited by 13zsmulAddGroupHomQuotientAddGroup.homQuotientZ…CITED BYCITES

Cites9

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

Cited by4

Results whose statement or proof uses this declaration.