Theorems · Theorem · category theory

StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app

∀ {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 : 𝓕.stalk p₀ ⟶ c)
  (U : (TopologicalSpace.Opens ↑X)ᵒᵖ),
  (StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf p₀ f).app U =
    if h : p₀ ∈ Opposite.unop U then
      CategoryTheory.CategoryStruct.comp (𝓕.germ (Opposite.unop U) p₀ h)
        (CategoryTheory.CategoryStruct.comp f (CategoryTheory.eqToHom ⋯))
    else (⋯ ▸ CategoryTheory.Limits.terminalIsTerminal).from (𝓕.obj U)

Defined in

Mathlib.Topology.Sheaves.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableCategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasColimits