Theorems · Theorem · category theory

CategoryTheory.Subfunctor.eq_sheafify_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 →
    (G = CategoryTheory.Subfunctor.sheafify J G ↔ CategoryTheory.Presieve.IsSheaf J G.toFunctor)

Defined in

Mathlib.CategoryTheory.Sites.Subsheaf

Cited by

2 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category