Theorems · Definition · category theory

CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.q

{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} →
                {data : F.OneHypercoverDenseData J₀ J X} →
                  {X₀ : C₀} →
                    {f : F.obj X₀ ⟶ X} →
                      {Y₀ : C₀} → {g : Y₀ ⟶ X₀} → (self : data.SieveStruct f g) → F.obj Y₀ ⟶ F.obj (data.X self.i₀)

the morphism that is part of the factorization fac.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

4 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category