Ph. Hackney, email@example.com
Peter LeFanu Lumsdaine, firstname.lastname@example.org
André Joyal, The Theory of Quasi-categories and its Applications
Various authors, Homotopy Type Theory
In class on November 18 Philip mentioned the model structure on Cat. Charles Rezk has a short proof of the existence of this model structure, http://www.math.uiuc.edu/~rezk/cat-ho.dvi. As for uniqueness, see this blog post and this mo comment.