Theorems · Theorem · group theory
Submonoid.gc_map_comap
∀ {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), GaloisConnection (Submonoid.map f) (Submonoid.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.
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- GaloisConnectionstatement · cited by 253
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement · cited by 190
- Submonoid.comapstatement · cited by 179
- Submonoid.map_le_iff_le_comapproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- Submonoid.le_comap_mapproof · cited by 24
- MonoidHom.map_mclosureproof · cited by 10
- Submonoid.gciMapComapproof · cited by 9
- Submonoid.giMapComapproof · cited by 9
- Submonoid.map_le_of_le_comapproof · cited by 7
- Submonoid.map_botproof · cited by 5
- Submonoid.map_supproof · cited by 4
- Submonoid.monotone_comapproof · cited by 4
- Submonoid.le_comap_of_map_leproof · cited by 3
- Submonoid.monotone_mapproof · cited by 3
- Submonoid.prod_eq_bot_iffproof · cited by 1
- Submonoid.comap_topproof · cited by 1