We provide a complete description of the category of pseudo-categories (including pseudo-functors, natural and pseudo-natural transformations and pseudo modifications). A pseudo-category is a non strict version of an internal category. It was called a weak category and weak double category in some earlier papers. When internal to Cat it is at the same time a generalization of a bicategory and a double category. The category of pseudo-categories is a kind of "tetracategory" and it turns out to be cartesian closed in a suitable sense.
Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 47-78 http://jhrs.rmi.acnet.ge/volumes/2006/n1a3/