Schreiber Synthetic Differential Jet Bundles are Reduced

An article that we are finalizing at CQTS, with I. Khavkine from CAS Prague:

---

• Grigorios Giotopoulos,$\;$ Igor Khavkine,$\;$ Hisham Sati $\;$and$\;$ Urs Schreiber:

  
  

  Synthetic Differential Jet Bundles are Reduced

  • manuscript: arXiv:2601.15862, pdf

Abstract: We have previously observed that the theory of solutions of partial differential equations, regarded as diffieties inside jet bundles, acquires a powerful comonadic formulation after passage from the category of Fréchet smooth manifolds to the Cahiers topos of formal smooth sets (a well-adapted model for Synthetic Differential Geometry). However, the tacit assumption that this passage preserves the projective limits that define infinite jet bundles had remained unproven. Here we provide a detailed proof.

Related articles:

• Synthetic Geometry of Differential Equations

• Field Theory via Higher Geometry II: Thickened Smooth Sets as Synthetic Foundations