Theorems · Definition · category theory

StalkSkyscraperPresheafAdjunctionAuxs.fromStalk

{X : TopCat} →
  (p₀ : ↑X) →
    [inst : (U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] →
      {C : Type v} →
        [inst_1 : CategoryTheory.Category.{u, v} C] →
          [inst_2 : CategoryTheory.Limits.HasTerminal C] →
            [inst_3 : CategoryTheory.Limits.HasColimits C] →
              {𝓕 : TopCat.Presheaf C X} → {c : C} → (𝓕 ⟶ skyscraperPresheaf p₀ c) → (𝓕.stalk p₀ ⟶ c)

If f : 𝓕 ⟶ skyscraperPresheaf p₀ c is a natural transformation, then there is a morphism 𝓕.stalk p₀ ⟶ c defined as the morphism from colimit to cocone at c.

Defined in

Mathlib.Topology.Sheaves.Skyscraper

Cited by

4 results in Mathlib

Foundations

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

Assumes

DecidableCategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasColimits