Higher Dimensional Enrichment
Category Theory
2007-05-23 v2 Algebraic Topology
Quantum Algebra
Abstract
Lyubashenko has described enriched 2-categories as categories enriched over V-Cat, the 2-category of categories enriched over a symmetric monoidal V. I have generalized this to the k-fold monoidal V. The symmetric case can easily be recovered. The introduction of this paper proposes a recursive definition of V-n-categories and their morphisms. Then I consider the special case of V-2-categories and give the details of the proof that with their morphisms these form the structure of a 3-category.
Cite
@article{arxiv.math/0306086,
title = {Higher Dimensional Enrichment},
author = {Stefan Forcey},
journal= {arXiv preprint arXiv:math/0306086},
year = {2007}
}
Comments
50 pages; complete definition of V-n-categories and morphisms between them; journal style and notation--note tensor^(1) replaces box^(2); updated references