A study of Penon weak n-categories Part 1: Monad interleaving

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We give an alternative construction of the monad used by Penon
to define weak n-categories. Penon’s monad adds two pieces of extra structure
to an n-globular set: a magma structure, giving composition, and a contraction
structure, giving coherence. We add these two structures using an
interleaving approach, following the method used by Cheng to construct Leinster’s
operad for weak ω-categories. We conclude by using our construction
to give an explicit description of the n-globular operad for Penon weak
Original languageEnglish
Pages (from-to)197-259
Number of pages63
JournalCahiers de Topologie et Géométrie Différentielle Catégoriques
Issue number3
Publication statusPublished - 1 Jan 2018


  • n-category
  • higher dimensional category
  • monad interleaving
  • monad
  • operad

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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