Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.yonedaCompSheafToPresheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      [inst_1 : J.Subcanonical] → J.yoneda.comp (CategoryTheory.sheafToPresheaf J (Type v)) ≅ CategoryTheory.yoneda

The yoneda embedding into the presheaf category factors through the one to the sheaf category.

Defined in

Mathlib.CategoryTheory.Sites.Canonical

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical