Theorems · Theorem · category theory

CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X Y : C}
  (f : X ⟶ Y) (x : CategoryTheory.Presieve.FamilyOfElements P (CategoryTheory.Presieve.singleton f)),
  x.Compatible ↔
    ∀ {Z : C} (p₁ p₂ : Z ⟶ X),
      CategoryTheory.CategoryStruct.comp p₁ f = CategoryTheory.CategoryStruct.comp p₂ f →
        (CategoryTheory.ConcreteCategory.hom (P.map p₁.op)) (x f ⋯) =
          (CategoryTheory.ConcreteCategory.hom (P.map p₂.op)) (x f ⋯)

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category