Theorems · Definition · group theory
multiplesHom
(M : Type u_1) → [inst : AddMonoid M] → M ≃ (ℕ →+ M)
Additive homomorphisms from ℕ are defined by the image of 1.
- Defined in
- Mathlib.Algebra.Group.Nat.Hom
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- zero_nsmulproof · cited by 137
- one_nsmulproof · cited by 63
- add_nsmulproof · cited by 44
Cited by10
Results whose statement or proof uses this declaration.
- AddSubmonoid.multiplesproof · cited by 40
- powersHomproof · cited by 6
- AddSubmonoid.closure_singleton_eqstatement and proof · cited by 2
- uliftMultiplesHomproof · cited by 2
- multiplesAddHomproof · cited by 2
- AddSubmonoid.one_eq_closureproof · cited by 1
- multiplesHom_applystatement · cited by 1
- multiplesHom_symm_applystatement · cited by 1
- AddMonoidHom.apply_natproof · cited by 0
- AddCommMonCat.adjproof · cited by 0