Brauer图、模算畴与电路代数的图神经定理
范畴论
2025-01-22 v3
摘要
电路代数用于研究有限型结不变量，是 Jones 平面代数的对称类比。它们与电路算畴密切相关，后者是模算畴的一种变体，允许额外的幺积。本文使用 Brauer 图范畴对电路代数进行了描述。利用迭代分配律和现有的模算畴神经定理，证明了电路算畴——进而电路代数——的抽象神经定理。
引用
@article{arxiv.2108.04557,
title = {Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras},
author = {Sophie Raynor},
journal= {arXiv preprint arXiv:2108.04557},
year = {2025}
}
备注
As of December 2024, this paper has been superceded by arXiv:2412.20260 (on circuit algebras, Brauer diagrams, modular operads and invariant theory) and arXiv:2412.20262 (on a graphical calculus, iterated distributive laws and nerve theorem for circuit algebras). The version below is from November 2022 (c.f., v2). It comprises 65 pages and many figures