---
title: "The Dual DG Category to Weinstein's symplectic \"category\" and applications to Geometric Quantization"
authors:
  - "Jonathan Weitsman"
year: 2026
venue: "arXiv:math.SG"
arxiv: "2608.09681"
doi: null
source: "https://arxiv.org/abs/2608.09681"
topics:
  - "curiosity"
  - "maths-foundations"
seed_rank: 1649
seed_batch: "curiosity-2026-09-09"
reviewed: "2026-09-09"
pool: "maths-foundations"
relevance_score: 10
lineage: symplectic-categories
cites:
  - title: "The Dual DG Category to Weinstein's symplectic \"category\" and applications to Geometric Quantization"
    url: "https://arxiv.org/abs/2608.09681"
    year: 2026
    arxiv: "2608.09681"
    doi: null
see:
  - "1583-symplectic-tiling-billiards-on-complete-affine-tori"
---

# The Dual DG Category to Weinstein's symplectic "category" and applications to Geometric Quantization

## One-sentence takeaway

Weinstein's symplectic "category" (canonical relations as morphisms) is only morally a category; this paper builds a true dg-category dual to it, with geometric-quantization applications.

## Why it's lovely

Why you might love this: everyone quotes Weinstein's symplectic "category" and then mumbles that morphisms do not always compose. Weitsman constructs an honest differential graded dual that restores composition and talks to geometric quantization. The rare paper that turns a community joke into a theorem.

## Key ideas

- Weinstein's symplectic "category": objects = symplectic manifolds, morphisms = canonical relations (not always composable).
- A true dg-category morally dual to that structure.
- Applications toward geometric quantization.
- Pairs with Legendrian / Floer / symplectic surface cards without reminting them.

## Caveats

dg-categorical; not a computational symplectic geometry toolkit. Heavy on foundations of geometric quantization.

## Links

- arXiv abs: https://arxiv.org/abs/2608.09681
- PDF: https://arxiv.org/pdf/2608.09681.pdf