English

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