Theorems · Definition · category theory

CategoryTheory.Sieve.functorPullback

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) → {X : C} → CategoryTheory.Sieve (F.obj X) → CategoryTheory.Sieve X

If R is a sieve, then the CategoryTheory.Presieve.functorPullback of R is actually a sieve.

Defined in

Mathlib.CategoryTheory.Sites.Sieves

Cited by

49 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category