Theorems · Theorem · group theory
AddSubgroup.gc_map_comap
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N),
GaloisConnection (AddSubgroup.map f) (AddSubgroup.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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- GaloisConnectionstatement · cited by 253
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.comapstatement · cited by 123
- AddSubgroup.map_le_iff_le_comapproof · cited by 10
Cited by12
Results whose statement or proof uses this declaration.
- AddMonoidHom.map_closureproof · cited by 8
- AddSubgroup.comap_topproof · cited by 7
- AddSubgroup.map_botproof · cited by 6
- AddSubgroup.map_eq_bot_iffproof · cited by 6
- AddSubgroup.map_supproof · cited by 5
- AddSubgroup.map_comap_leproof · cited by 2
- AddSubgroup.relIndex_map_mapproof · cited by 1
- AddSubgroup.le_comap_mapproof · cited by 1
- AddSubgroup.map_iSupproof · cited by 1
- AddSubgroup.closure_piproof · cited by 0
- AddSubgroup.comap_iInfproof · cited by 0
- AddSubgroup.comap_infproof · cited by 0