Theorems · Definition · category theory

CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (J : CategoryTheory.GrothendieckTopology C) →
          (K : CategoryTheory.GrothendieckTopology D) →
            (G : CategoryTheory.Functor C D) →
              {A : Type u_4} →
                [inst_2 : CategoryTheory.Category.{v_4, u_4} A] →
                  [inst_3 : CategoryTheory.Functor.IsDenseSubsite J K G] →
                    [inst_4 : (G.sheafPushforwardContinuous A J K).IsEquivalence] →
                      [inst_5 : CategoryTheory.HasWeakSheafify J A] →
                        {P : CategoryTheory.Functor Dᵒᵖ A} →
                          {Q : CategoryTheory.Sheaf K A} →
                            ((CategoryTheory.Functor.IsDenseSubsite.sheafifyOfIsEquivalence J K G A).obj P ⟶ Q) ≃
                              (P ⟶ Q.obj)

Auxiliary definition for sheafifyAdjunctionOfIsEquivalence.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

4 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsiteCategoryTheory.Functor.IsEquivalenceCategoryTheory.HasWeakSheafify