Comparison of models for (∞,n)–categories, I

Bergner, Julia E¹ ; Rezk, Charles²

¹ Department of Mathematics, University of California Riverside, 900 University Avenue, Riverside, CA 92521, USA
² Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 West Green Street, Urbana, IL 61801, USA

Geometry & topology, Tome 17 (2013) no. 4, pp. 2163-2202.

Résumé

While many different models for $\left(\infty ,1\right)$–categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $\left(\infty ,n\right)$–categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as $\left(\infty ,n\right)$–categories. Furthermore, we establish Quillen equivalences between them.

Détail

DOI : 10.2140/gt.2013.17.2163

Classification : 55U40, 55U35, 18D15, 18D20, 18G30, 18C10
Keywords: $(\infty, n)$–categories, $\Theta_n$–spaces, enriched categories

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