Theorems · Theorem · category theory

CategoryTheory.Presheaf.isSheaf_iff_isSheaf_comp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {A : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} A]
  {B : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} B] (J : CategoryTheory.GrothendieckTopology C)
  (P : CategoryTheory.Functor Cᵒᵖ A) (s : CategoryTheory.Functor A B)
  [CategoryTheory.Limits.HasLimitsOfSize.{v₁, max v₁ u₁, v₂, u₂} A]
  [CategoryTheory.Limits.PreservesLimitsOfSize.{v₁, max v₁ u₁, v₂, v₃, u₂, u₃} s] [s.ReflectsIsomorphisms],
  CategoryTheory.Presheaf.IsSheaf J P ↔ CategoryTheory.Presheaf.IsSheaf J (P.comp s)

Defined in

Mathlib.CategoryTheory.Sites.Sheaf

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfSizeCategoryTheory.Limits.PreservesLimitsOfSizeCategoryTheory.Functor.ReflectsIsomorphisms