Theorems · Definition · group theory
Submonoid.map
{M : Type u_1} →
{N : Type u_2} →
[inst : MulOneClass M] →
[inst_1 : MulOneClass N] →
{F : Type u_4} → [inst_2 : FunLike F M N] → [mc : MonoidHomClass F M N] → F → Submonoid M → Submonoid NThe image of a Submonoid along a MonoidHom is a Submonoid.
- Cited by
- 190 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 61 definitions · uses no axioms
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
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassstatement and proof · cited by 244
Cited by214
Results whose statement or proof uses this declaration.
- Subgroup.mapproof · cited by 301
- Algebra.algebraMapSubmonoidproof · cited by 137
- MonoidHom.mrangeproof · cited by 63
- Subring.mapproof · cited by 33
- Subgroup.ofUnitsproof · cited by 31
- Subsemiring.mapproof · cited by 29
- pinGroupproof · cited by 25
- Submonoid.le_comap_mapstatement · cited by 24
- Submonoid.gc_map_comapstatement · cited by 16
- IsLocalization.ringEquivOfRingEquivstatement and proof · cited by 15
- RingHom.LocalizationPreservesproof · cited by 13
- MonoidHom.mrange_eq_mapstatement · cited by 13
Showing the 200 most cited of 214.