Theorems · Theorem · group theory
Subgroup.gc_map_comap
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N),
GaloisConnection (Subgroup.map f) (Subgroup.comap f)- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- GaloisConnectionstatement · cited by 253
- Subgroup.comapstatement · cited by 154
- Subgroup.map_le_iff_le_comapproof · cited by 13
Cited by12
Results whose statement or proof uses this declaration.
- MonoidHom.map_closureproof · cited by 16
- Subgroup.comap_topproof · cited by 10
- Subgroup.map_botproof · cited by 10
- Subgroup.map_eq_bot_iffproof · cited by 7
- Subgroup.map_supproof · cited by 7
- Subgroup.map_comap_leproof · cited by 3
- Subgroup.map_iSupproof · cited by 2
- Subgroup.comap_iInfproof · cited by 1
- Subgroup.le_comap_mapproof · cited by 1
- Subgroup.relIndex_map_mapproof · cited by 0
- Subgroup.closure_piproof · cited by 0
- Subgroup.comap_infproof · cited by 0