Theorems · Definition · group theory
AddSubsemigroup.map
{M : Type u_1} → {N : Type u_2} → [inst : Add M] → [inst_1 : Add N] → (M →ₙ+ N) → AddSubsemigroup M → AddSubsemigroup NThe image of an AddSubsemigroup along an AddSemigroup homomorphism is
an AddSubsemigroup.
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- AddHomstatement and proof · cited by 294
- AddSubsemigroupstatement and proof · cited by 262
Cited by56
Results whose statement or proof uses this declaration.
- AddHom.srangeproof · cited by 17
- AddSubsemigroup.gc_map_comapstatement · cited by 15
- AddSubsemigroup.gciMapComapstatement · cited by 9
- AddSubsemigroup.giMapComapstatement · cited by 9
- AddHom.srange_eq_mapstatement · cited by 2
- AddHom.subsemigroupMapstatement · cited by 2
- AddEquiv.subsemigroupMapstatement and proof · cited by 2
- AddSubsemigroup.equivMapOfInjectivestatement · cited by 1
- AddSubsemigroup.le_prod_iffstatement and proof · cited by 1
- AddSubsemigroup.map_comap_eqstatement and proof · cited by 1
- AddSubsemigroup.map_equiv_eq_comap_symmstatement and proof · cited by 1
- AddSubsemigroup.map_le_iff_le_comapstatement · cited by 1