Theorems · Theorem · category theory

StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk_assoc

∀ {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 ⟶ skyscraperPresheaf p₀ c)
  (U : TopologicalSpace.Opens ↑X) (hU : p₀ ∈ U) {Z : C} (h : c ⟶ Z),
  CategoryTheory.CategoryStruct.comp (𝓕.germ U p₀ hU)
      (CategoryTheory.CategoryStruct.comp (StalkSkyscraperPresheafAdjunctionAuxs.fromStalk p₀ f) h) =
    CategoryTheory.CategoryStruct.comp (f.app (Opposite.op U))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯) h)

Defined in

Mathlib.Topology.Sheaves.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableCategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasColimits