## Generalized enrichment of categories (1999)

Venue: | Also Journal of Pure and Applied Algebra |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Leinster99generalizedenrichment,

author = {Tom Leinster},

title = {Generalized enrichment of categories},

journal = {Also Journal of Pure and Applied Algebra},

year = {1999},

pages = {391--406}

}

### OpenURL

### 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.