Theorems · Theorem · category theory

CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_and_equalizerCondition

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {A : Type u₃}
  [inst_1 : CategoryTheory.Category.{v₃, u₃} A] (F : CategoryTheory.Functor Cᵒᵖ A)
  [inst_2 : CategoryTheory.Preregular C] [inst_3 : CategoryTheory.FinitaryExtensive C]
  [h : ∀ {Y X : C} (f : Y ⟶ X) [CategoryTheory.EffectiveEpi f], CategoryTheory.Limits.HasPullback f f],
  CategoryTheory.Presheaf.IsSheaf (CategoryTheory.coherentTopology C) F ↔
    CategoryTheory.Limits.PreservesFiniteProducts F ∧ CategoryTheory.regularTopology.EqualizerCondition F

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

5 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreregularCategoryTheory.FinitaryExtensiveCategoryTheory.Limits.HasPullback