Theorems · Definition · group theory
Submonoid.giMapComap
{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 : F} → Function.Surjective ⇑f → GaloisInsertion (Submonoid.map f) (Submonoid.comap f)map f and comap f form a GaloisInsertion when f is surjective.
- 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
- Submonoidstatement · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement · cited by 190
- Submonoid.comapstatement · cited by 179
- GaloisInsertionstatement · cited by 35
- Submonoid.gc_map_comapproof · cited by 16
- GaloisConnection.toGaloisInsertionproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- Submonoid.map_comap_eq_of_surjectiveproof · cited by 1
- Submonoid.map_surjective_of_surjectiveproof · cited by 0
- Submonoid.map_iInf_comap_of_surjectiveproof · cited by 0
- Submonoid.map_iSup_comap_of_surjectiveproof · cited by 0
- Submonoid.map_inf_comap_of_surjectiveproof · cited by 0
- Submonoid.comap_injective_of_surjectiveproof · cited by 0
- Submonoid.comap_le_comap_iff_of_surjectiveproof · cited by 0
- Submonoid.comap_strictMono_of_surjectiveproof · cited by 0
- Submonoid.map_sup_comap_of_surjectiveproof · cited by 0