Theorems · Theorem · category theory

CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_hom_ext

∀ {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} {Z : A}
  {f g : Z ⟶ CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj data G₀ X},
  (∀ (i : (data X).I₀),
      CategoryTheory.CategoryStruct.comp f
          (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ data G₀ X i) =
        CategoryTheory.CategoryStruct.comp g
          (CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ data G₀ X i)) →
    f = g

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

5 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfSize