Theorems · Definition · category theory

CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso

{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) →
                          (X₀ : C₀) →
                            (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheaf data G₀).obj
                                (Opposite.op (F.obj X₀)) ≅
                              G₀.obj.obj (Opposite.op X₀)

The presheaf presheaf data G₀ extends G₀.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

5 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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