Theorems · Theorem · category theory

CategoryTheory.Presheaf.IsSheaf.hom_ext_ofArrows

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {A : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} A]
  {J : CategoryTheory.GrothendieckTopology C} {P : CategoryTheory.Functor Cᵒᵖ A},
  CategoryTheory.Presheaf.IsSheaf J P →
    ∀ {I : Type u_1} {S : C} {X : I → C} (f : (i : I) → X i ⟶ S),
      CategoryTheory.Sieve.ofArrows X f ∈ J S →
        ∀ {E : A} {x y : E ⟶ P.obj (Opposite.op S)},
          (∀ (i : I),
              CategoryTheory.CategoryStruct.comp x (P.map (f i).op) =
                CategoryTheory.CategoryStruct.comp y (P.map (f i).op)) →
            x = y

Defined in

Mathlib.CategoryTheory.Sites.Sheaf

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category