  The bulk of this paper is devoted to the comparison of several models for the
theory of (infinity,2)-categories: that is, higher categories in which all
k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is
also considered). Our ultimate goal is to lay the foundations for a study of
Tom Goodwillie's calculus of functors. To this end, we have included some
simple applications to the theory of first derivatives.
