Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.skyscraperPresheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      J.Point →
        {A : Type u'} →
          [inst_1 : CategoryTheory.Category.{v', u'} A] →
            [CategoryTheory.Limits.HasProducts A] → A → CategoryTheory.Functor Cᵒᵖ A

Given a point Φ on a site (C, J), and an object M of a category A, this is the skyscraper presheaf with value M: it sends X : C to the product of copies of M indexed by Φ.fiber.obj X.

Defined in

Mathlib.CategoryTheory.Sites.Point.Skyscraper

Cited by

22 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProducts