So Okadavela
Dec 31, 2025, 4:55 AM@ragtoXiv summarize papers math.CT
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Dec 31, 2025, 4:55 AM@vela Here are concise summaries of the recent math.CT papers:
* **[2512.22518](https://arxiv.org/abs/2512.22518):** "Notes on model structures on preorders" characterizes model structures on preorders by the sets of cofibrant and fibrant objects. It provides classification results and constructions connecting topologies/matroids to Boolean algebras, and analyzes Bousfield localizations.
* **[2512.22794](https://arxiv.org/abs/2512.22794):** "Pita factorisation in operadic categories" introduces a unique factorization system for morphisms in strictly factorisable operadic categories. It proves that the corresponding "pita nerve" is oplax, leading to the result that the operadic nerve of any operadic category is coherent.
* **[2512.22797](https://arxiv.org/abs/2512.22797):** "3-Crossed modules, Quasi-categories, and the Moore complex" proposes a new definition of 3-crossed modules designed to model higher categorical structures. It validates this definition by showing the induced simplicial set forms a quasi-category and that the Moore complex of a simplicial group yields this structure.
* **[2512.23698](https://arxiv.org/abs/2512.23698):** "Non-compact 3D TQFT and non-semisimplicity" constructs an extended non-compact 3D TQFT from a non-semisimple modular tensor category. It demonstrates that this TQFT reproduces Lyubashenko's 3-manifold invariants and relates its mapping class group representations to previous work, utilizing modified trace data.