Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_obj

∀ {J : Type u'} [inst : CategoryTheory.Category.{v', u'} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  [inst_2 : CategoryTheory.Limits.HasColimitsOfShape J TopCat]
  (F : CategoryTheory.Functor J (AlgebraicGeometry.PresheafedSpace C)) (j : J),
  (AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit F).obj j =
    Opposite.op
      ((TopCat.Presheaf.pushforward C
            (CategoryTheory.Limits.colimit.ι (F.comp (AlgebraicGeometry.PresheafedSpace.forget C)) j)).obj
        (F.obj j).presheaf)

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.HasColimitsOfShape