Theorems · Definition · group theory
AddSubmonoid.comap
{M : Type u_1} →
{N : Type u_2} →
[inst : AddZeroClass M] →
[inst_1 : AddZeroClass N] →
{F : Type u_4} → [inst_2 : FunLike F M N] → [mc : AddMonoidHomClass F M N] → F → AddSubmonoid N → AddSubmonoid MThe preimage of an AddSubmonoid along an AddMonoidHom is an AddSubmonoid.
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 15 from the axioms · 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.preimageproof · cited by 4,946
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
Cited by73
Results whose statement or proof uses this declaration.
- Submodule.comapproof · cited by 347
- AddSubgroup.comapproof · cited by 123
- AddSubmonoid.addUnitsproof · cited by 32
- Subsemiring.comapproof · cited by 20
- AddMonoidHom.mkerproof · cited by 19
- AddSubmonoid.gc_map_comapstatement · cited by 16
- NonUnitalSubsemiring.comapproof · cited by 14
- AddSubmonoid.gciMapComapstatement · cited by 9
- AddSubmonoid.giMapComapstatement · cited by 9
- AddSubmonoid.mem_comapstatement · cited by 8
- AddSubmonoid.LocalizationMap.ofAddEquivOfDomproof · cited by 6
- AddSubmonoid.map_le_of_le_comapstatement · cited by 4