Leinster, T. (2002) Generalized enrichment of categories. Journal of Pure and Applied Algebra, 168(2-3), pp. 391-406. (doi: 10.1016/S0022-4049(01)00105-0)
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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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Leinster, Dr Tom |
| Authors: | Leinster, T. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Pure and Applied Algebra |
| ISSN: | 0022-4049 |
| ISSN (Online): | 1873-1376 |
| Published Online: | 11 February 2002 |
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