Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Garner, Richard, Shulman, Michael
Institutions: Macquarie University, Institute for Advanced Study
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Research in Mathematics
OpenAlex ID: W2952654017