A study of Penon weak n-categories Part 2: A multisimplicial nerve construction

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In this paper we take the first step towards a comparison between
an algebraic and a non-algebraic definition of weak n-category. This comparison takes the form of a nerve functor, the established method of moving from the algebraic setting to the non-algebraic setting. The algebraic definition we use is that due to Penon, and the non-algebraic definition we use is Simpson’s variant of Tamsamani’s definition. As a prototype for our nerve
construction, we recall a nerve construction for bicategories proposed by Leinster, and prove that the nerve of a bicategory given by this construction is
a Tamsamani–Simpson weak 2-category. We then define our nerve functor
for Penon weak n-categories. We prove that the nerve of a Penon weak 2-
category is a Tamsamani–Simpson weak 2-category, and conjecture that this
result holds for higher n.
Original languageEnglish
Pages (from-to)32-114
JournalCahiers de Topologie et Géométrie Différentielle Catégoriques
Issue number1
Publication statusPublished - 2019


  • n-category
  • higher-dimensional category
  • nerve construction

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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