  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 via functional equations and
operads. In addition, we compute the differentials of the forgetful functor
from the category of $n$-Poisson algebras in terms of the homology of
configuration spaces.

Algebraic Topology;Category Theory