English

On the loop space of a 2-category

Algebraic Topology 2011-08-29 v2

Abstract

Every small category CC has a classifying space BCBC 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 B2CB_2C of a 2-category CC and prove that, under certain conditions, the loop space ΩcB2C\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.

Keywords

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

R2 v1 2026-06-21T15:20:04.821Z