English

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.

Keywords

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

R2 v1 2026-06-21T22:55:27.826Z