  The Goodwillie tower is based on the idea of approximating a functor F by a
series of functors satisfying the strong property of "n-excision". In this
dissertation, we study a weaker property of "n-additivity" and compare the two.
Theorem 9.1, one of the main results in this dissertation, establishes that if
$F$ is reasonably good, there is a fibration sequence with the fiber being the
realization of a simplicial space built from a cotriple made of iterated cross
effects and base space the "discrete" degree $n$ additive approximation to $F$.
We also relate the construction given to Goodwillie's construction, and give
conditions under which they coincide.
