A Quillen model structure for 2-categories

We describe a cofibrantly generated Quillen model structure on the locally finitely presentable category 2-Cat of (small) 2-categories and 2-functors; the weak equivalences are the biequivalences, and the homotopy relation on 2-functors is just pseudonatural equivalence. The model structure is proper, and is compatible with the monoidal structure given by the Gray tensor product. It is not compatible with the Cartesian closed structure, in which the tensor product is the product. The model structure restricts to a model structure on the full subcategory PsGpd of 2-Cat, consisting of those 2-categories in which every arrow is an equivalence and every 2-cell is invertible. The model structure on PsGpd is once again proper, and compatible with the monoidal structure given by the Gray tensor product.