Gabriel's pull-up/push-down decomposition #
This file identifies the explicit coproduct model for pull-up of push-down with the bundled pull-up functor and with the formal module shifts attached to a chosen shift core.
noncomputable def
MagnitudeConjecture.CoveringHom.linearOrbitPullupPushdownIso
{k : Type uK}
[Field k]
{C : Type u}
[CategoryTheory.Category.{v, u} C]
[CategoryTheory.Preadditive C]
[CategoryTheory.Linear k C]
{A : Type w}
[AddGroup A]
[CategoryTheory.HasShift C A]
[∀ (a : A), (CategoryTheory.shiftFunctor C a).Additive]
[∀ (a : A), CategoryTheory.Functor.Linear k (CategoryTheory.shiftFunctor C a)]
(M : LinearModuleCategory k)
:
(linearOrbitPullupPushdownTranslateCofan M).pt ≅ linearModuleOrbitPullup.obj (linearModuleOrbitPushdown.obj M)
The explicit coproduct object is the bundled pull-up of the bundled push-down.