Some properties of the theory of n-categories

Abstract

Let $L_n$ denote the Dwyer-Kan localization of the category of weak n-categories divided by the n-equivalences. We propose a list of properties that this simplicial category is likely to have, and conjecture that these properties characterize $L_n$ up to equivalence. We show, using these properties, how to obtain the morphism $n-1$-categories between two points in an object of $L_n$ and how to obtain the composition map between the morphism objects.