Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910055310295040 |
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| author | Auinger, Karl Volkov, Mikhail |
| author_facet | Auinger, Karl Volkov, Mikhail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_01016 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic Auinger, Karl Volkov, Mikhail Category Theory Group Theory Geometric Topology 57N70 20M07 08B05 18B40 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. |
| title | Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic |
| topic | Category Theory Group Theory Geometric Topology 57N70 20M07 08B05 18B40 |
| url | https://arxiv.org/abs/2002.01016 |