Theorems · Theorem · category theory

TopCat.Presheaf.germ_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X : TopCat}
  {FC : C → C → Type u_1} {CC : C → Type v} [inst_2 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)]
  [instCC : CategoryTheory.ConcreteCategory C FC] (F : TopCat.Presheaf C X) {U V : TopologicalSpace.Opens ↑X} {x : ↑X}
  {hxU : x ∈ U} {hxV : x ∈ V} (W : TopologicalSpace.Opens ↑X),
  x ∈ W →
    ∀ (iWU : W ⟶ U) (iWV : W ⟶ V) {sU : CategoryTheory.ToType (F.obj (Opposite.op U))}
      {sV : CategoryTheory.ToType (F.obj (Opposite.op V))},
      (CategoryTheory.ConcreteCategory.hom (F.map iWU.op)) sU =
          (CategoryTheory.ConcreteCategory.hom (F.map iWV.op)) sV →
        (CategoryTheory.ConcreteCategory.hom (F.germ U x hxU)) sU =
          (CategoryTheory.ConcreteCategory.hom (F.germ V x hxV)) sV

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsFunLikeCategoryTheory.ConcreteCategory