Cubical n-Categories and Finite Limits Theories

Details Cubical n-Categories and Finite Limits Theories Cubical n-Categories and Finite Limits Theories

2010-01-15

arxiv.org/abs/1001.2628v1

Mathematics

Category Theory

14 pages; submitted to proceedings of MakkaiFest 2009; expository

Scientific paper

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.

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