Theorems · Definition · category theory

CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {G : CategoryTheory.Functor C D} →
          {A : Type w} →
            [inst_2 : CategoryTheory.Category.{w', w} A] →
              {J : CategoryTheory.GrothendieckTopology C} →
                {K : CategoryTheory.GrothendieckTopology D} →
                  [G.IsCocontinuous J K] →
                    {F : CategoryTheory.Functor Cᵒᵖ A} →
                      CategoryTheory.Presheaf.IsSheaf J F →
                        {R : CategoryTheory.Functor Dᵒᵖ A} →
                          (G.op.comp R ⟶ F) →
                            {X : D} →
                              {S : K.Cover X} →
                                (s : CategoryTheory.Limits.Multifork (S.index R)) →
                                  {Y : C} → (G.obj Y ⟶ X) → (s.pt ⟶ F.obj (Opposite.op Y))

Auxiliary definition for lift.

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

5 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCocontinuous