TY - JOUR

T1 - A cartesian presentation of weak n-categories

AU - Rezk, Charles

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.2140/gt.2010.14.521

DO - 10.2140/gt.2010.14.521

M3 - Article

AN - SCOPUS:77953693060

VL - 14

SP - 521

EP - 571

JO - Geometry and Topology

JF - Geometry and Topology

SN - 1364-0380

IS - 1

ER -