Theorems · Theorem · category theory

CategoryTheory.Functor.sheafAdjunctionCocontinuous_unit_app_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),
  ((G.sheafAdjunctionCocontinuous A J K).unit.app F).hom = (G.op.ranAdjunction A).unit.app F.obj

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

2 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