Theorems · Theorem · category theory

CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc

∀ {C₀ : Type u₀} {C : Type u} [inst : CategoryTheory.Category.{v₀, u₀} C₀] [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor C₀ C} {J₀ : CategoryTheory.GrothendieckTopology C₀}
  {J : CategoryTheory.GrothendieckTopology C} {A : Type u'} [inst_2 : CategoryTheory.Category.{v', u'} A]
  [inst_3 : CategoryTheory.Functor.IsDenseSubsite J₀ J F] (data : (X : C) → F.OneHypercoverDenseData J₀ J X)
  [inst_4 : CategoryTheory.Limits.HasLimitsOfSize.{w, w, v', u'} A] (G₀ : CategoryTheory.Sheaf J₀ A) {X Y : C} {X₀ : C₀}
  (f : F.obj X₀ ⟶ X) (g : X ⟶ Y) {Z : A} (h : G₀.obj.obj (Opposite.op X₀) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap data G₀ g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction data G₀ f)
        h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction data G₀
        (CategoryTheory.CategoryStruct.comp f g))
      h

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsiteCategoryTheory.Limits.HasLimitsOfSize