#### Volume 17, issue 4 (2013)

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Comparison of models for $(\infty, n)$–categories, I

### Julia E Bergner and Charles Rezk

Geometry & Topology 17 (2013) 2163–2202
##### Abstract

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.

##### Keywords
$(\infty, n)$–categories, $\Theta_n$–spaces, enriched categories
##### Mathematical Subject Classification 2010
Primary: 55U40
Secondary: 55U35, 18D15, 18D20, 18G30, 18C10