Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.stalkMap_germ_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C]
  {X Y : AlgebraicGeometry.PresheafedSpace C} (α : X ⟶ Y) (U : TopologicalSpace.Opens ↑↑Y) (x : ↑↑X)
  (hx : (CategoryTheory.ConcreteCategory.hom α.base) x ∈ U) {Z : C} (h : X.presheaf.stalk x ⟶ Z),
  CategoryTheory.CategoryStruct.comp (Y.presheaf.germ U ((CategoryTheory.ConcreteCategory.hom α.base) x) hx)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.Hom.stalkMap α x) h) =
    CategoryTheory.CategoryStruct.comp (α.c.app (Opposite.op U))
      (CategoryTheory.CategoryStruct.comp (X.presheaf.germ ((TopologicalSpace.Opens.map α.base).obj U) x hx) h)

Defined in

Mathlib.Geometry.RingedSpace.Stalks

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits