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# Homology, Homotopy and Applications

## Volume 15 (2013)

### Number 2

### $n$-relative categories: a model for the homotopy theory of $n$-fold homotopy theories

Pages: 281 – 300

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a17

#### Authors

#### Abstract

We introduce, for every integer $n \geq 1$, the notion of an $n$-relative category and show that the category of the small $n$-relative categories is a model for the homotopy theory of $n$-fold homotopy theories, i.e., homotopy theories of… homotopy theories.

#### Keywords

relative category, $n$-relative category, higher category

#### 2010 Mathematics Subject Classification

18D05, 18G55

Published 4 December 2014