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Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.map_comap_eq_of_surjective

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {f : L.Hom M N},
  Function.Surjective ⇑f →
    ∀ (S : L.Substructure N), FirstOrder.Language.Substructure.map f (FirstOrder.Language.Substructure.comap f S) = S
Defined in
Mathlib.ModelTheory.Substructures
Cited by
0 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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DFunLike.coe · cited by 62936DFunLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Hom · cited by 107Language.HomFirstOrder.Language.Substructure.map · cited by 49Substructure.mapGaloisInsertion.l_u_eq · cited by 37GaloisInsertion.l_u_eqFirstOrder.Language.Substructure.comap · cited by 31Substructure.comapFirstOrder.Language.Substructure.giMapComap · cited by 9Substructure.giMapComapSubstructure.map_comap_eq_of_…CITED BYCITES

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