Theorems · Theorem · category theory

CategoryTheory.Subfunctor.isSheaf_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  {F : CategoryTheory.Functor Cᵒᵖ (Type w)} (G : CategoryTheory.Subfunctor F),
  CategoryTheory.Presieve.IsSheaf J F →
    (CategoryTheory.Presieve.IsSheaf J G.toFunctor ↔
      ∀ (U : Cᵒᵖ) (s : F.obj U), G.sieveOfSection s ∈ J (Opposite.unop U) → s ∈ G.obj U)

Defined in

Mathlib.CategoryTheory.Sites.Subsheaf

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category