feat: the free presheaf of modules functor#14245
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PR summary 2db5f3a243Import changesNo significant changes to the import graph
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(See #16755 for a more polished version of this construction.)
This is very much a draft. Proofs are terrible (because of issues with automation/simp in categories of modules).
We define the free presheaf of modules functor
(Cᵒᵖ ⥤ Type u) ⥤ PresheafOfModules.{u} Sand show it is left adjoint to the forget functor.Then, given
X : C, we show the morphisms from the free presheaf of modules on the presheaf of typesyoneda.obj Xto any presheaf of modulesMidentifies to the sectionsM(X).Then, the idea would be to show the existence of the left adjoint of the pushforward functor by using that any presheaf of modules is a colimit of such free presheaves of modules on yoneda presheaves.
This contribution was created as part of the AIM workshop "Formalizing algebraic geometry" in June 2024.