The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories
| dc.creator | Cheng, Eugenia | |
| dc.creator | Gurski, Nick | |
| dc.date | 2007-08-08 | |
| dc.date.accessioned | 2026-07-07T08:22:52Z | |
| dc.date.available | 2026-07-07T08:22:52Z | |
| dc.description | We examine the periodic table of weak n-categories for the low-dimensional cases. It is widely understood that degenerate categories give rise to monoids, doubly degenerate bicategories to commutative monoids, and degenerate bicategories to monoidal categories; however, to understand this correspondence fully we examine the totalities of such structures together with maps between them and higher maps between those. Categories naturally form a 2-category {\bfseries Cat} so we take the full sub-2-category of this whose 0-cells are the degenerate categories. Monoids naturally form a category, but we regard this as a discrete 2-category to make the comparison. We show that this construction does not yield a biequivalence; to get an equivalence we ignore the natural transformations and consider only the {\it category} of degenerate categories. A similar situation occurs for degenerate bicategories. The tricategory of such does not yield an equivalence with monoidal categories; we must consider only the categories of such structures. For doubly degenerate bicategories the tricategory of such is not naturally triequivalent to the category of commutative monoids (regarded as a tricategory). However in this case considering just the categories does not give an equivalence either; to get an equivalence we consider the {\it bicategory} of doubly degenerate bicategories. We conclude with a hypothesis about how the above cases might generalise for n-fold degenerate n-categories. | |
| dc.description | 23 pages, to appear in Streetfest proceedings | |
| dc.identifier | https://arxiv.org/abs/0708.1178 | |
| dc.identifier | http://arxiv.org/abs/0708.1178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135798 | |
| dc.subject | Category Theory | |
| dc.subject | 18D05, 18D10 | |
| dc.title | The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories | |
| dc.type | text |