Goodwillie Calculi

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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.