Theorems · Theorem · category theory

CategoryTheory.isSheaf_coherent

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Precoherent C]
  (P : CategoryTheory.Functor Cᵒᵖ (Type w)),
  CategoryTheory.Presieve.IsSheaf (CategoryTheory.coherentTopology C) P ↔
    ∀ (B : C) (α : Type) [Finite α] (X : α → C) (π : (a : α) → X a ⟶ B),
      CategoryTheory.EffectiveEpiFamily X π →
        CategoryTheory.Presieve.IsSheafFor P (CategoryTheory.Presieve.ofArrows X π)

Defined in

Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Precoherent