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arXiv · 2601.15862

Synthetic Differential Jet Bundles are Reduced

Grigorios Giotopoulos·Igor Khavkine·Hisham Sati·Urs Schreiber
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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 Fr\'echet 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.

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Grigorios Giotopoulos, Igor Khavkine, Hisham Sati, Urs Schreiber. 2026-01-22. Synthetic Differential Jet Bundles are Reduced. https://arxiv.org/abs/2601.15862

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