Enriched categories as a free cocompletion
Abstract
This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory -- categorifying the classical theory of categories enriched in a monoidal category -- up to a description of the free cocompletion of an enriched bicategory under a class of weighted bicolimits. The second objective is to describe a universal property of the process assigning to a monoidal category V the equipment of V-enriched categories, functors, transformations, and modules; we do so by considering, more generally, the assignation sending an equipment C to the equipment of C-enriched categories, functors, transformations, and modules, and exhibiting this as the free cocompletion of a certain kind of enriched bicategory under a certain class of weighted bicolimits.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2013
- DOI:
- 10.48550/arXiv.1301.3191
- arXiv:
- arXiv:1301.3191
- Bibcode:
- 2013arXiv1301.3191G
- Keywords:
-
- Mathematics - Category Theory;
- 18D20;
- 18D05;
- 18A35
- E-Print:
- 80 pages