Generalized enrichment of categories
Abstract
We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal categories and ordinary multicategories. Enrichment in an fc-multicategory extends the (more or less well-known) theories of enrichment in a monoidal category, in a bicategory, and in a multicategory. Moreover, fc-multicategories provide a natural setting for the bimodules construction, traditionally performed on suitably cocomplete bicategories. Although this paper is elementary and self-contained, we also explain why, from one point of view, fc-multicategories are the natural structures in which to enrich categories.
Cite
@article{arxiv.math/0204279,
title = {Generalized enrichment of categories},
author = {Tom Leinster},
journal= {arXiv preprint arXiv:math/0204279},
year = {2007}
}
Comments
18 pages; written 1999