%0 Journal Article
%T A note on the Penon definition of $n$-category
%A Eugenia Cheng
%A Michael Makkai
%J Mathematics
%D 2009
%I arXiv
%X We show that doubly degenerate Penon tricategories give symmetric rather than braided monoidal categories. We prove that Penon tricategories cannot give all tricategories, but we show that a slightly modified version of the definition rectifies the situation. We give the modified definition, using non-reflexive rather than reflexive globular sets, and show that the problem with doubly degenerate tricategories does not arise.
%U http://arxiv.org/abs/0907.3961v1