Theorems · Theorem · category theory

CategoryTheory.Presheaf.IsSheaf.isSeparated

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {A : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} A]
  {J : CategoryTheory.GrothendieckTopology C} {F : CategoryTheory.Functor Cᵒᵖ A} {FA : A → A → Type u_1}
  {CA : A → Type u_2} [inst_2 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)]
  [inst_3 : CategoryTheory.ConcreteCategory A FA] [J.HasSheafCompose (CategoryTheory.forget A)],
  CategoryTheory.Presheaf.IsSheaf J F → CategoryTheory.Presheaf.IsSeparated J F

Defined in

Mathlib.CategoryTheory.Sites.Whiskering

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.GrothendieckTopology.HasSheafCompose