Theorems · Definition · category theory

CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso

{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) →
                  [inst_3 : G.IsCocontinuous J K] →
                    [inst_4 : ∀ (F : CategoryTheory.Functor Cᵒᵖ A), G.op.HasPointwiseRightKanExtension F] →
                      (G.sheafPushforwardCocontinuous A J K).comp (CategoryTheory.sheafToPresheaf K A) ≅
                        (CategoryTheory.sheafToPresheaf J A).comp G.op.ran

G.sheafPushforwardCocontinuous A J K : Sheaf J A ⥤ Sheaf K A is induced by the right Kan extension functor G.op.ran on presheaves.

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

5 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCocontinuousCategoryTheory.Functor.HasPointwiseRightKanExtension