Geometry & Topology

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

Abstract

While many different models for $(∞,1)$–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 $(∞,n)$–categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as $(∞,n)$–categories. Furthermore, we establish Quillen equivalences between them.

Article information

Source
Geom. Topol., Volume 17, Number 4 (2013), 2163-2202.

Dates
Revised: 18 March 2013
Accepted: 17 April 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732649

Digital Object Identifier
doi:10.2140/gt.2013.17.2163

Mathematical Reviews number (MathSciNet)
MR3109865

Zentralblatt MATH identifier
1273.18031

Citation

Bergner, Julia E; Rezk, Charles. Comparison of models for $(\infty, n)$–categories, I. Geom. Topol. 17 (2013), no. 4, 2163--2202. doi:10.2140/gt.2013.17.2163. https://projecteuclid.org/euclid.gt/1513732649

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