  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.
