Abstract:We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V. This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases. We then describe the appropriate notion of "limit" for such enriched indexed categories, and show that they admit "free cocompletions" constructed as usual with a Yoneda embedding.
| Comments: | 80 pages. v2: minor changes; final journal version. v3: fix bug in diagram code |
| Subjects: | Category Theory (math.CT) |
| MSC classes: | 18D20, 18D30 |
| Cite as: | arXiv:1212.3914 [math.CT] |
| (or arXiv:1212.3914v3 [math.CT] for this version) | |
| https://doi.org/10.48550/arXiv.1212.3914 arXiv-issued DOI via DataCite |
|
| Journal reference: | Theory Appl. Categ. 28 (2013) 616-695 |
Submission history
From: Michael Shulman [view email]
[v1]
Mon, 17 Dec 2012 08:02:23 UTC (88 KB)
[v2]
Tue, 6 Aug 2013 17:53:43 UTC (85 KB)
[v3]
Fri, 6 Jun 2014 21:29:38 UTC (85 KB)