Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso_naturality

∀ {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 P' : CategoryTheory.Functor Cᵒᵖ A} (F : P ⟶ P'),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.GrothendieckTopology.IsLocalSite.point J).presheafFiber.map F)
      (CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso J P').hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso J P).hom
      (F.app (Opposite.op (⊤_ C)))

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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