Weak complicial sets, a simplicial weak omega-category theory. Part I: basic homotopy theory
| dc.creator | Verity, Dominic | |
| dc.date | 2006-04-19 | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T07:11:04Z | |
| dc.date.available | 2026-07-07T07:11:04Z | |
| dc.description | This paper develops the foundations of a simplicial theory of weak omega-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets provides a common generalisation of the theories of (strict) omega-categories, Kan complexes and Joyal's quasi-categories. We generalise a number of results due to the current author with regard to complicial sets and strict omega-categories to provide an armoury of well behaved technical devices, such as joins and Gray tensor products, which will be used to study these the weak omega-category theory of these structures in a series of companion papers. In particular, we establish their basic homotopy theory by constructing a Quillen model structure on the category of stratified simplicial sets whose fibrant objects are the weak complicial sets. As a simple corollary of this work we provide an independent construction of Joyal's model structure on simplicial sets for which the fibrant objects are the quasi-categories. | |
| dc.description | 65 pages, further updates to the material on quasi-categories, minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0604414 | |
| dc.identifier | http://arxiv.org/abs/math/0604414 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111618 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Topology | |
| dc.subject | 18D05, 55U10 (Primary) 18D15, 18D20, 18D35, 18F99, 18G30 (Secondary) | |
| dc.title | Weak complicial sets, a simplicial weak omega-category theory. Part I: basic homotopy theory | |
| dc.type | text |