On the loop space of a 2-category
Algebraic Topology
2011-08-29 v2
Abstract
Every small category has a classifying space 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 of a 2-category and prove that, under certain conditions, the loop space 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.
Cite
@article{arxiv.1005.1300,
title = {On the loop space of a 2-category},
author = {Matias L. del Hoyo},
journal= {arXiv preprint arXiv:1005.1300},
year = {2011}
}
Comments
21 pages, final version. Section 8 concerning the main theorem was rewritten. In particular, a partial converse for the main theorem was added