Theorems · Definition · category theory

CategoryTheory.Functor.OneHypercoverDenseData.sieve

{C₀ : Type u₀} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v₀, u₀} C₀] →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {F : CategoryTheory.Functor C₀ C} →
          {J₀ : CategoryTheory.GrothendieckTopology C₀} →
            {J : CategoryTheory.GrothendieckTopology C} →
              {X : C} → F.OneHypercoverDenseData J₀ J X → {X₀ : C₀} → (F.obj X₀ ⟶ X) → CategoryTheory.Sieve X₀

Given data : OneHypercoverDenseData F J₀ J X and a morphism f : F.obj X₀ ⟶ X, this is the sieve of X₀ consisting of morphisms g : Y₀ ⟶ X₀ such that there exists i₀ : data.I₀, q : F.obj Y₀ ⟶ F.obj (data.X i₀) such that we have a factorization q ≫ data.f i₀ = F.map g ≫ f.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

3 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category