Theorems · Definition · group theory
AddSubmonoid.gciMapComap
{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 : F} → Function.Injective ⇑f → GaloisCoinsertion (AddSubmonoid.map f) (AddSubmonoid.comap f)map f and comap f form a GaloisCoinsertion when f is injective.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- AddSubmonoid.mapstatement · cited by 99
- AddSubmonoid.comapstatement · cited by 62
- GaloisCoinsertionstatement · cited by 35
- AddSubmonoid.gc_map_comapproof · cited by 16
- GaloisConnection.toGaloisCoinsertionproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- AddSubmonoid.map_injective_of_injectiveproof · cited by 1
- AddSubmonoid.comap_map_eq_of_injectiveproof · cited by 0
- AddSubmonoid.map_le_map_iff_of_injectiveproof · cited by 0
- AddSubmonoid.comap_sup_map_of_injectiveproof · cited by 0
- AddSubmonoid.comap_surjective_of_injectiveproof · cited by 0
- AddSubmonoid.map_strictMono_of_injectiveproof · cited by 0
- AddSubmonoid.comap_iInf_map_of_injectiveproof · cited by 0
- AddSubmonoid.comap_iSup_map_of_injectiveproof · cited by 0
- AddSubmonoid.comap_inf_map_of_injectiveproof · cited by 0