Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.comap_comap

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} {P : Type u_2} [inst : L.Structure M] [inst_1 : L.Structure N]
  [inst_2 : L.Structure P] (S : L.Substructure P) (g : L.Hom N P) (f : L.Hom M N),
  FirstOrder.Language.Substructure.comap f (FirstOrder.Language.Substructure.comap g S) =
    FirstOrder.Language.Substructure.comap (g.comp f) S

Defined in: Mathlib.ModelTheory.Substructures
Cited by: 0 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext
Assumes: FirstOrder.Language.Structure FirstOrder.Language.Structure FirstOrder.Language.Structure

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FirstOrder.Languagestatement and proof · cited by 1,084
FirstOrder.Language.Structurestatement and proof · cited by 775
FirstOrder.Language.Substructurestatement and proof · cited by 242
FirstOrder.Language.Homstatement and proof · cited by 107
FirstOrder.Language.Substructure.comapstatement · cited by 31
FirstOrder.Language.Hom.compstatement · cited by 20

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