Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_obj

∀ {J : Type u'} [inst : CategoryTheory.Category.{v', u'} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  (F : CategoryTheory.Functor J (AlgebraicGeometry.PresheafedSpace C)) [inst_2 : CategoryTheory.Limits.HasColimit F]
  (U : TopologicalSpace.Opens ↑↑(CategoryTheory.Limits.colimit F)) (j : Jᵒᵖ),
  (AlgebraicGeometry.PresheafedSpace.componentwiseDiagram F U).obj j =
    (F.obj (Opposite.unop j)).presheaf.obj
      (Opposite.op ((TopologicalSpace.Opens.map (CategoryTheory.Limits.colimit.ι F (Opposite.unop j)).base).obj U))

Defined in

Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit