∀ {X : TopCat} (p₀ : ↑X) [inst : (U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] {C : Type v}
  [inst_1 : CategoryTheory.Category.{w, v} C] [inst_2 : CategoryTheory.Limits.HasTerminal C] {a b : C} (f : a ⟶ b)
  (U : (TopologicalSpace.Opens ↑X)ᵒᵖ),
  (SkyscraperPresheafFunctor.map' p₀ f).app U =
    if h : p₀ ∈ Opposite.unop U then
      CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯)
        (CategoryTheory.CategoryStruct.comp f (CategoryTheory.eqToHom ⋯))
    else (⋯ ▸ CategoryTheory.Limits.terminalIsTerminal).from ((skyscraperPresheaf p₀ a).obj U)