arXiv 2002.010162020-02math.CTmath.GRmath.GT

2-cobordism的组合骨架与环形范畴及其在等式逻辑中的应用

Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic

Karl Auinger, Mikhail Volkov

备注：: Version 2 is radically reworked and substantially extended and should therefore be considered essentially a new paper. 95 pages, 13 numbered figures and many unnumbered illustrations, 1 table

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AI总结：

本文提出编码所有2-cobordism类的组合数据，并证明其局部monoids无有限公理化等式理论，同时构造了该范畴的von-Neumann-正则扩展。

摘要：

我们介绍了一组完整的组合数据，用于编码所有2-cobordism类的范畴2Cob。作为应用，我们证明了2Cob的局部monoids不具有可有限公理化的等式理论。作为另一个应用，我们构造了该范畴的von-Neumann-正则扩展。类似的结果也适用于拓扑环形范畴以及后者的一些商范畴，如仿射Temperley-Lieb范畴。

英文摘要：

We introduce a complete set of combinatorial data that encode the category $2\mathfrak{Cob}$ of all $2$-cobordisms. As an application, we show that the local monoids of $2\mathfrak{Cob}$ do not have finitely axiomatizable equational theories. As yet another application, we construct a von-Neumann-regular extension of this category. Similar results are provided for the topological annular category and various quotients of the latter, like the affine Temperley--Lieb category.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。