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Main Authors: Auinger, Karl, Volkov, Mikhail
Format: Preprint
Published: 2020
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Online Access:https://arxiv.org/abs/2002.01016
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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