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

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

2009-07-23

arxiv.org/abs/0907.3961v1

Mathematics

Category Theory

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

Scientific paper

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.

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