Theorems · Definition · category theory

CategoryTheory.Presheaf.coherentExtensiveEquivalence

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {A : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} A] →
        [inst_2 : CategoryTheory.Preregular C] →
          [inst_3 : CategoryTheory.FinitaryExtensive C] →
            [∀ (X : C), CategoryTheory.Projective X] →
              CategoryTheory.Sheaf (CategoryTheory.coherentTopology C) A ≌
                CategoryTheory.Sheaf (CategoryTheory.extensiveTopology C) A

The categories of coherent sheaves and extensive sheaves on C are equivalent if C is preregular, finitary extensive, and every object is projective.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

11 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreregularCategoryTheory.FinitaryExtensiveCategoryTheory.Projective