Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map

∀ {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' : J} (f : j ⟶ j'),
  (AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit F).map f =
    (CategoryTheory.CategoryStruct.comp
        ((TopCat.Presheaf.pushforward C
              (CategoryTheory.Limits.colimit.ι (F.comp (AlgebraicGeometry.PresheafedSpace.forget C)) j')).map
          (F.map f).c)
        (CategoryTheory.CategoryStruct.comp
          (TopCat.Presheaf.Pushforward.comp ((F.comp (AlgebraicGeometry.PresheafedSpace.forget C)).map f)
              (CategoryTheory.Limits.colimit.ι (F.comp (AlgebraicGeometry.PresheafedSpace.forget C)) j')
              (F.obj j).presheaf).inv
          (TopCat.Presheaf.pushforwardEq ⋯ (F.obj j).presheaf).hom)).op

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