(Infinity,2)-Categories and the Goodwillie Calculus I

Understand

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.