A cartesian presentation of weak n-categories

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We propose a notion of weak (n+k;n)-category, which we call (n+k,n)-Θ-spaces. The (n+k,n)-Θ-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal's category Θn. This notion is a generalization of that of complete Segal spaces (which are precisely the (∞, 1)-Θ-spaces). Our main result is that the above model category is cartesian.

Original languageEnglish (US)
Pages (from-to)521-571
Number of pages51
JournalGeometry and Topology
Issue number1
StatePublished - 2010

ASJC Scopus subject areas

  • Geometry and Topology


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