Theorems · Theorem · category theory

CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom

∀ {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 : C)
  (i : (data X).I₀),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap data G₀ ((data X).f i))
      (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso data G₀ ((data X).X i)).hom =
    CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ data G₀ X i

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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