Theorems · Theorem · group theory
AddSubmonoid.gc_map_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 : F),
GaloisConnection (AddSubmonoid.map f) (AddSubmonoid.comap f)- Cited by
- 16 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- GaloisConnectionstatement · cited by 253
- AddMonoidHomClassstatement and proof · cited by 252
- AddSubmonoid.mapstatement · cited by 99
- AddSubmonoid.comapstatement · cited by 62
- AddSubmonoid.map_le_iff_le_comapproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- AddMonoidHom.map_mclosureproof · cited by 12
- AddSubmonoid.gciMapComapproof · cited by 9
- AddSubmonoid.giMapComapproof · cited by 9
- AddSubmonoid.map_botproof · cited by 4
- AddSubmonoid.map_le_of_le_comapproof · cited by 4
- AddSubmonoid.map_supproof · cited by 4
- AddSubmonoid.comap_topproof · cited by 1
- AddSubmonoid.prod_eq_bot_iffproof · cited by 1
- AddSubmonoid.monotone_mapproof · cited by 1
- AddSubmonoid.comap_map_comapproof · cited by 0
- AddSubmonoid.map_comap_leproof · cited by 0
- AddSubmonoid.map_comap_mapproof · cited by 0