Enriched indexed categories
Category Theory
2014-06-10 v3
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.
Cite
@article{arxiv.1212.3914,
title = {Enriched indexed categories},
author = {Michael Shulman},
journal= {arXiv preprint arXiv:1212.3914},
year = {2014}
}
Comments
80 pages. v2: minor changes; final journal version. v3: fix bug in diagram code