Theorems · Theorem · category theory

CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_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]
  (data : (X : C) → F.OneHypercoverDenseData J₀ J X) [inst_3 : CategoryTheory.Limits.HasLimitsOfSize.{w, w, v', u'} A]
  (G₀ : CategoryTheory.Sheaf J₀ A) (X : C) (i i' : (data X).I₀) (j : (data X).I₁ i i') {Z : A}
  (h : G₀.obj.obj (Opposite.op ((data X).Y j)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ data G₀ X i)
      (CategoryTheory.CategoryStruct.comp (G₀.obj.map ((data X).p₁ j).op) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ data G₀ X i')
      (CategoryTheory.CategoryStruct.comp (G₀.obj.map ((data X).p₂ j).op) h)

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfSize