Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {A : Type u'}
  [inst_1 : CategoryTheory.Category.{v', u'} A] (H : J.OneHypercoverFamily) (P : CategoryTheory.Functor Cᵒᵖ A)
  [H.IsGenerating],
  CategoryTheory.Presheaf.IsSheaf J P ↔
    ∀ ⦃X : C⦄ (E : J.OneHypercover X), H E → Nonempty (CategoryTheory.Limits.IsLimit (E.multifork P))

Defined in

Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsGenerating