  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.

Category Theory