Theorems · Theorem · category theory

CategoryTheory.Presheaf.isSheaf_iff_multifork

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {A : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} A]
  (J : CategoryTheory.GrothendieckTopology C) (P : CategoryTheory.Functor Cᵒᵖ A),
  CategoryTheory.Presheaf.IsSheaf J P ↔
    ∀ (X : C) (S : J.Cover X), Nonempty (CategoryTheory.Limits.IsLimit (S.multifork P))

Defined in

Mathlib.CategoryTheory.Sites.Sheaf

Cited by

5 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category