Theorems · Theorem · category theory

CategoryTheory.regularTopology.isSheaf_of_projective

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (F : CategoryTheory.Functor Cᵒᵖ D)
  [inst_2 : CategoryTheory.Preregular C] [∀ (X : C), CategoryTheory.Projective X],
  CategoryTheory.Presheaf.IsSheaf (CategoryTheory.regularTopology C) F

Every presheaf is a sheaf for the regular topology if every object of C is projective.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreregularCategoryTheory.Projective