Theorems · Definition · category theory

CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.casesOn

{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} →
                          {motive : data.SieveStruct f g → Sort u_1} →
                            (t : data.SieveStruct f g) →
                              ((i₀ : data.I₀) →
                                  (q : F.obj Y₀ ⟶ F.obj (data.X i₀)) →
                                    (fac :
                                        CategoryTheory.CategoryStruct.comp q (data.f i₀) =
                                          CategoryTheory.CategoryStruct.comp (F.map g) f) →
                                      motive { i₀ := i₀, q := q, fac := fac }) →
                                motive t

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense

Cited by

0 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category