Theorems · Definition · category theory

CategoryTheory.Sieve.shrinkFunctor

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v₁, u₁} C] →
      {X : C} → CategoryTheory.Sieve X → CategoryTheory.Subfunctor (CategoryTheory.shrinkYoneda.{w, v₁, u₁}.obj X)

If C is w-locally small, any sieve induces a subfunctor of shrinkYoneda.{w}.obj X.

Defined in

Mathlib.CategoryTheory.Sites.Sieves

Cited by

14 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall