In this talk, I will show that the category of algebraically cofibrant 2-categories (= the category of coalgebras for the normal pseudofunctor classifier comonad on 2-Cat) admits a model structure left-induced from Lack's model structure for 2-categories, whose full subcategory of fibrant objects is equivalent to the category of bicategories and normal pseudofunctors. Like the model structure for 2-categories, this induced model structure is monoidal with respect to the Gray tensor product, but unlike the model structure for 2-categories, the induced model structure is moreover cartesian