A note on the Penon definition of $n$-category
Category Theory
2009-07-24 v1
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.
Keywords
Cite
@article{arxiv.0907.3961,
title = {A note on the Penon definition of $n$-category},
author = {Eugenia Cheng and Michael Makkai},
journal= {arXiv preprint arXiv:0907.3961},
year = {2009}
}
Comments
14 pages, to appear in Cahiers de Topologie et Geometrie Differentielle Categoriques