Theorems · Theorem · category theory

germ_skyscraperPresheafStalkOfSpecializes_hom

∀ {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]
  [inst_3 : CategoryTheory.Limits.HasColimits C] {y : ↑X} (h : p₀ ⤳ y) (U : TopologicalSpace.Opens ↑X) (hU : y ∈ U),
  CategoryTheory.CategoryStruct.comp ((skyscraperPresheaf p₀ A).germ U y hU)
      (skyscraperPresheafStalkOfSpecializes p₀ A h).hom =
    CategoryTheory.eqToHom ⋯

Defined in

Mathlib.Topology.Sheaves.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableCategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasColimits