Cubical n-Categories and Finite Limits Theories
arXiv:1001.2628
Abstract
This note informally describes a way to build certain cubical n-categories by iterating a process of taking models of certain finite limits theories. We base this discussion on a construction of "double bicategories" as bicategories internal to Bicat, and see how to extend this to n-tuple bicategories (and similarly for tricategories etc.) We briefly consider how to reproduce "simpler" definitions of weak cubical n-category from these.
14 pages; submitted to proceedings of MakkaiFest 2009; expository