---
title: "3-dimensional TQFTs from derived categories of quantum group representations"
authors:
  - "Cris Negron"
year: 2026
venue: "arXiv:math.QA"
arxiv: "2608.10285"
doi: null
source: "https://arxiv.org/abs/2608.10285"
topics:
  - "curiosity"
  - "maths-foundations"
seed_rank: 1617
seed_batch: "curiosity-2026-09-07"
reviewed: "2026-09-07"
pool: "maths-foundations"
relevance_score: 10
lineage: tqft
cites:
  - title: "3-dimensional TQFTs from derived categories of quantum group representations"
    url: "https://arxiv.org/abs/2608.10285"
    year: 2026
    arxiv: "2608.10285"
    doi: null
see:
  - "1546-all-once-extended-3d-tqfts-are-reshetikhin-turaev-theories"
---

# 3-dimensional TQFTs from derived categories of quantum group representations

## One-sentence takeaway

For any finite modular tensor category A, the derived ∞-category D(A) carries a 3D TQFT — surfaces marked by A-objects, values in spectra/categories.

## Why it's lovely

Why you might love this: once-extended 3D TQFTs met Reshetikhin–Turaev on the library shelf (1546); here the input is the *derived* ∞-category of a modular tensor category, so quantum-group representation theory feeds a derived TQFT rather than only its heart.

## Key ideas

- Input: finite modular tensor category A.
- Output: symmetric monoidal functor from an ∞-category of marked surfaces into a derived/categorical target built from D(A).
- Extends the modular-category → 3D TQFT pipeline past the abelian heart.
- Sits beside once-extended RT recognition (1546).

## Caveats

Finite MTC hypothesis; derived enrichment is the point and the cost. Not a lattice-surgery cookbook.

## Implications for Broadside

Deepens the TQFT shelf: derived coefficients for 3D theories, relevant whenever Broadside toys with categorical state spaces.

## Links

- arXiv abs: https://arxiv.org/abs/2608.10285
- PDF: https://arxiv.org/pdf/2608.10285.pdf