A note on the Penon definition of $n$-category

Abstract

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.

14 pages, to appear in Cahiers de Topologie et Geometrie Differentielle Categoriques

References in corpus (1)

• The periodic table of $n$-categories for low dimensions II: degenerate tricategories