Enriched indexed categories

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.

80 pages. v2: minor changes; final journal version. v3: fix bug in diagram code

References in corpus (3)

• Duality and traces for indexed monoidal categories
• Exact completions and small sheaves
• Enriched categories as a free cocompletion

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