Theorems · Theorem · group theory
Submonoid.le_comap_map
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] (S : Submonoid M) {F : Type u_4}
[inst_2 : FunLike F M N] [mc : MonoidHomClass F M N] {f : F}, S ≤ Submonoid.comap f (Submonoid.map f S)- Cited by
- 24 results in Mathlib
- Foundations
- Depth 26 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
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement · cited by 190
- Submonoid.comapstatement · cited by 179
- GaloisConnection.le_u_lproof · cited by 52
- Submonoid.gc_map_comapproof · cited by 16
Cited by24
Results whose statement or proof uses this declaration.
- Module.Finite.of_isLocalizationproof · cited by 10
- IsLocalization.map_injective_of_injectivestatement · cited by 6
- Algebra.algebraMapSubmonoid_le_comapproof · cited by 5
- isIntegral_localizationstatement and proof · cited by 4
- IsLocalization.algebraMap_eq_map_map_submonoidstatement and proof · cited by 3
- RingHom.isIntegralElem_localization_at_leadingCoeffstatement and proof · cited by 2
- IsLocalization.ker_mapstatement and proof · cited by 2
- IsLocalization.map_surjective_of_surjectivestatement · cited by 2
- FractionalIdeal.le_one_of_extendedHom_le_oneproof · cited by 2
- localizationAlgebraMap_defstatement · cited by 1
- RingHom.toKerIsLocalization_isLocalizedModulestatement and proof · cited by 1
- IsLocalization.algebraMap_apply_eq_map_map_submonoidstatement · cited by 1