Theorems · Definition · category theory

CategoryTheory.Presieve.IsSheafFor.extend

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X : C} →
      {S : CategoryTheory.Sieve X} →
        {P : CategoryTheory.Functor Cᵒᵖ (Type v₁)} →
          CategoryTheory.Presieve.IsSheafFor P S.arrows → (S.functor ⟶ P) → (CategoryTheory.yoneda.obj X ⟶ P)

If P is a sheaf for the sieve S on X, a natural transformation from S (viewed as a functor) to P can be (uniquely) extended to all of yoneda.obj X. `` f S → P ↓ ↗ yX ``

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category