Theorems · Theorem · category theory

CategoryTheory.presheafHom_isSheafFor

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} A]
  (F G : CategoryTheory.Functor Cᵒᵖ A) {X : C} (S : CategoryTheory.Sieve X)
  (hG :
    ⦃Y : C⦄ →
      (f : Y ⟶ X) → CategoryTheory.Limits.IsLimit (G.mapCone (CategoryTheory.Sieve.pullback f S).arrows.cocone.op)),
  CategoryTheory.Presieve.IsSheafFor (CategoryTheory.presheafHom F G) S.arrows

Defined in

Mathlib.CategoryTheory.Sites.SheafHom

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category