On the loop space of a 2-category

Details On the loop space of a 2-category On the loop space of a 2-category

2010-05-07

arxiv.org/abs/1005.1300v2

Journal of Pure and Applied Algebra 216 (2012), pp. 28-40

Mathematics

Algebraic Topology

21 pages, final version. Section 8 concerning the main theorem was rewritten. In particular, a partial converse for the main t

Scientific paper

10.1016/j.jpaa.2011.05.001

Every small category $C$ has a classifying space $BC$ associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper we study the classifying space $B_2C$ of a 2-category $C$ and prove that, under certain conditions, the loop space $\Omega_c B_2C$ can be recovered up to homotopy from the endomorphisms of a given object. We also present several subsidiary results that we develop to prove our main theorem.

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