Theorems · Theorem · category theory

TopCat.Presheaf.pullbackPushforwardAdjunction_unit_app_app_germToPullbackStalk

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X Y : TopCat}
  (f : X ⟶ Y) (F : TopCat.Presheaf C Y) (V : (TopologicalSpace.Opens ↑Y)ᵒᵖ) (x : ↑X)
  (hx : (CategoryTheory.ConcreteCategory.hom f) x ∈ Opposite.unop V),
  CategoryTheory.CategoryStruct.comp (((TopCat.Presheaf.pullbackPushforwardAdjunction C f).unit.app F).app V)
      (TopCat.Presheaf.germToPullbackStalk C f F ((TopologicalSpace.Opens.map f).obj (Opposite.unop V)) x hx) =
    F.germ (Opposite.unop V) ((CategoryTheory.ConcreteCategory.hom f) x) hx

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits