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Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.gc_map_comap

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] (f : L.Hom M N),
  GaloisConnection (FirstOrder.Language.Substructure.map f) (FirstOrder.Language.Substructure.comap f)
Defined in
Mathlib.ModelTheory.Substructures
Cited by
14 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.Substructure.gciMapComap · cited by 9Substructure.gciMapComapFirstOrder.Language.Substructure.giMapComap · cited by 9Substructure.giMapComapFirstOrder.Language.Substructure.map_iSup · cited by 1Substructure.map_iSupFirstOrder.Language.Substructure.monotone_comap · cited by 0Substructure.monotone_com…FirstOrder.Language.Substructure.monotone_map · cited by 0Substructure.monotone_mapFirstOrder.Language.Substructure.le_comap_map · cited by 0Substructure.le_comap_mapFirstOrder.Language.Substructure.le_comap_of_map_le · cited by 0Substructure.le_comap_of_…FirstOrder.Language.Substructure.map_bot · cited by 0Substructure.map_botFirstOrder.Language.Substructure.map_comap_le · cited by 0Substructure.map_comap_leFirstOrder.Language.Substructure.map_comap_map · cited by 0Substructure.map_comap_mapFirstOrder.Language.Substructure.comap_iInf · cited by 0Substructure.comap_iInfFirstOrder.Language.Substructure.comap_inf · cited by 0Substructure.comap_infFirstOrder.Language.Substructure.map_le_of_le_comap · cited by 0Substructure.map_le_of_le…FirstOrder.Language.Substructure.map_sup · cited by 0Substructure.map_supFirstOrder.Language.Substructure.comap_map_comap · cited by 0Substructure.comap_map_co…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureGaloisConnection · cited by 253GaloisConnectionFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Hom · cited by 107Language.HomFirstOrder.Language.Substructure.map · cited by 49Substructure.mapFirstOrder.Language.Substructure.comap · cited by 31Substructure.comapFirstOrder.Language.Substructure.map_le_iff_le_comap · cited by 3Substructure.map_le_iff_l…Substructure.gc_map_comapCITED BYCITES

Cites8

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Cited by16

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