Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberNatIso

{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] →
                (CategoryTheory.GrothendieckTopology.IsLocalSite.point J).presheafFiber ≅
                  (CategoryTheory.evaluation Cᵒᵖ A).obj (Opposite.op (⊤_ C))

The presheaf fibre functor of point J is given by evaluation at the terminal object.

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

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Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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