Theorems · Definition · category theory

skyscraperPresheafCoconeIsColimitOfSpecializes

{X : TopCat} →
  (p₀ : ↑X) →
    [inst : (U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] →
      {C : Type v} →
        [inst_1 : CategoryTheory.Category.{u, v} C] →
          (A : C) →
            [inst_2 : CategoryTheory.Limits.HasTerminal C] →
              {y : ↑X} → (h : p₀ ⤳ y) → CategoryTheory.Limits.IsColimit (skyscraperPresheafCoconeOfSpecializes p₀ A h)

The cocone at A for the stalk functor of skyscraperPresheaf p₀ A when y ∈ closure {p₀} is a colimit

Defined in

Mathlib.Topology.Sheaves.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableCategoryTheory.CategoryCategoryTheory.Limits.HasTerminal