Theorems · Definition · group theory
Subsemigroup.map
{M : Type u_1} → {N : Type u_2} → [inst : Mul M] → [inst_1 : Mul N] → (M →ₙ* N) → Subsemigroup M → Subsemigroup NThe image of a subsemigroup along a semigroup homomorphism is a subsemigroup.
- Cited by
- 51 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
- Subsemigroupstatement and proof · cited by 323
- MulHomstatement and proof · cited by 299
Cited by60
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.mapproof · cited by 22
- NonUnitalSubring.mapproof · cited by 19
- MulHom.srangeproof · cited by 16
- Subsemigroup.gc_map_comapstatement · cited by 15
- Subsemigroup.gciMapComapstatement · cited by 9
- Subsemigroup.giMapComapstatement · cited by 9
- MulHom.subsemigroupMapstatement · cited by 2
- MulEquiv.subsemigroupMapstatement and proof · cited by 2
- RingEquiv.nonUnitalSubsemiringMapproof · cited by 2
- Subsemigroup.map_le_iff_le_comapstatement · cited by 1
- Subsemigroup.map_mapstatement and proof · cited by 1
- MulHom.srange_eq_mapstatement · cited by 1