Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.coconstantSheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      [CategoryTheory.LocallySmall.{w, v, u} C] →
        [J.IsLocalSite] →
          (A : Type u') →
            [inst_3 : CategoryTheory.Category.{v', u'} A] →
              [CategoryTheory.Limits.HasProducts A] → CategoryTheory.Functor A (CategoryTheory.Sheaf J A)

The right adjoint to the global sections functor that exists over any local site. This is implemented as the skyscraper functor associated to point.{w} J, but can be thought of as taking any object X : A to the sheaf that sends each Y : C to the product over copies of A indexed by the points ⊤_ C ⟶ Y of Y. Note this takes in an extra universe parameter w that does not appear in the output type A ⥤ Sheaf J A but is required for the construction; it should always be given explicitly when referring to this functor, as in e.g. coconstantSheaf.{w} J A.

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.GrothendieckTopology.IsLocalSiteCategoryTheory.CategoryCategoryTheory.Limits.HasProducts