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

Authors

C. Barwick (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

D. M. Kan (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

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

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Published 4 December 2014