We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors F : A â†’ MA from a pointed category with coproducts to A-modules in terms of differentials of F . Here A is a commutative S-algebra. We specialize to the case when A is the category of a-algebras for an operad a and F isâ€¦ (More)

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed, and their Taylor towers are computed. We also show that these functors factor through objects enriched over the homology of little n-cubes operads and discuss the relationship between functors defined viaâ€¦ (More)