Theorems · Definition · category theory

CategoryTheory.Presheaf.IsSheaf

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {A : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} A] →
        CategoryTheory.GrothendieckTopology C → CategoryTheory.Functor Cᵒᵖ A → Prop

A sheaf of A is a presheaf P : Cᵒᵖ ⥤ A such that for every E : A, the presheaf of types given by sending U : C to Hom_{A}(E, P U) is a sheaf of types.

Defined in

Mathlib.CategoryTheory.Sites.Sheaf

Cited by

991 results in Mathlib

Foundations

Depth 33 from the axioms, rests on 308 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category