Theorems · Theorem · commutative algebra
Ideal.gc_map_comap
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[inst_3 : RingHomClass F R S], GaloisConnection (Ideal.map f) (Ideal.comap f)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 27 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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Ideal.mapstatement · cited by 692
- Ideal.comapstatement · cited by 443
- GaloisConnectionstatement · cited by 253
- RingHomClassstatement and proof · cited by 193
- Ideal.map_le_iff_le_comapproof · cited by 60
Cited by17
Results whose statement or proof uses this declaration.
- Ideal.map_mapproof · cited by 37
- Ideal.le_comap_mapproof · cited by 17
- Ideal.comap_topproof · cited by 15
- Ideal.map_comap_leproof · cited by 14
- Ideal.map_botproof · cited by 12
- Ideal.map_idproof · cited by 11
- Ideal.map_le_of_le_comapproof · cited by 6
- Ideal.le_comap_of_map_leproof · cited by 4
- Ideal.map_supproof · cited by 3
- Ideal.comap_map_comapproof · cited by 3
- Ideal.comap_sInfproof · cited by 2
- Ideal.map_inf_leproof · cited by 1