Theorems · Theorem · category theory

CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_hom

∀ {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] [inst_5 : G.IsContinuous J K]
  {F : CategoryTheory.Sheaf K A} {H : CategoryTheory.Sheaf J A} (f : (G.sheafPushforwardContinuous A J K).obj F ⟶ H),
  (((G.sheafAdjunctionCocontinuous A J K).homEquiv F H) f).hom = ((G.op.ranAdjunction A).homEquiv F.obj H.obj) f.hom

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCocontinuousCategoryTheory.Functor.HasPointwiseRightKanExtensionCategoryTheory.Functor.IsContinuous