Theorems · Theorem · category theory

CategoryTheory.Sheaf.adjunction_unit_app_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] {E : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} E]
  {F : CategoryTheory.Functor D E} {G : CategoryTheory.Functor E D} [inst_3 : CategoryTheory.HasWeakSheafify J D]
  [inst_4 : J.HasSheafCompose F] (adj : G ⊣ F) (X : CategoryTheory.Sheaf J E),
  ((CategoryTheory.Sheaf.adjunction J adj).unit.app X).hom =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Adjunction.whiskerRight Cᵒᵖ adj).unit.app X.obj)
      (CategoryTheory.Functor.whiskerRight (CategoryTheory.toSheafify J (X.obj.comp G)) F)

Defined in

Mathlib.CategoryTheory.Sites.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.HasSheafCompose