Enrichment as Categorical Delooping I: Enrichment Over Iterated Monoidal Categories
| dc.creator | Forcey, Stefan | |
| dc.date | 2003-04-02 | |
| dc.date | 2003-10-23 | |
| dc.date.accessioned | 2026-07-07T04:56:34Z | |
| dc.date.available | 2026-07-07T04:56:34Z | |
| dc.description | The 2-category V-Cat of categories enriched over a braided monoidal category V is not itself braided in any way that is based upon the braiding of V. The exception is the case in which V is symmetric, which leads to V-Cat being symmetric as well. This paper describes how these facts are related to a categorical analogue of topological delooping. It seems that the analogy of loop spaces is a good guide for how to define the concept of enrichment over various types of monoidal objects, including k-fold monoidal categories and their higher dimensional counterparts. The main result is that for V a k-fold monoidal category, V-Cat becomes a (k-1)-fold monoidal 2-category in a canonical way. I indicate how this process may be iterated by enriching over V-Cat, along the way defining the 3-category of categories enriched over V-Cat. | |
| dc.description | 52 pages; additional comments on braided V in section 3; updated references, citations, and typos; journal style and notation--note tensor^(1) replaces box^(2) | |
| dc.identifier | https://arxiv.org/abs/math/0304026 | |
| dc.identifier | http://arxiv.org/abs/math/0304026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66965 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 18D10; 18D20 | |
| dc.title | Enrichment as Categorical Delooping I: Enrichment Over Iterated Monoidal Categories | |
| dc.type | text |