Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.toPresheafFiber_pointPresheafFiberIso_hom_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] [inst_2 : J.IsLocalSite] {A : Type u'}
  [inst_3 : CategoryTheory.Category.{v', u'} A] [inst_4 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A]
  {P : CategoryTheory.Functor Cᵒᵖ A} (X : C) (x : (CategoryTheory.GrothendieckTopology.IsLocalSite.point J).fiber.obj X)
  {Z : A} (h : P.obj (Opposite.op (⊤_ C)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.GrothendieckTopology.IsLocalSite.point J).toPresheafFiber X x P)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso J P).hom h) =
    CategoryTheory.CategoryStruct.comp (P.map (CategoryTheory.shrinkCoyonedaObjObjEquiv x).op) h

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.GrothendieckTopology.IsLocalSiteCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize