#
Enriched indexed categories

##
Michael Shulman

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.

Keywords:
monoidal category, enriched category, indexed category, fibered
category

2010 MSC:
18D20,18D30

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 21, pp 616-695.

http://www.tac.mta.ca/tac/volumes/28/21/28-21.pdf

Revised 2022-03-28. Original version at

http://www.tac.mta.ca/tac/volumes/28/21/28-21a.pdf

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