Theorems · Theorem · category theory

CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensive

∀ {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.FinitaryPreExtensive C],
  CategoryTheory.Presheaf.IsSheaf (CategoryTheory.coherentTopology C) F ↔
    CategoryTheory.Presheaf.IsSheaf (CategoryTheory.extensiveTopology C) F ∧
      CategoryTheory.Presheaf.IsSheaf (CategoryTheory.regularTopology C) F

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreregularCategoryTheory.FinitaryPreExtensive