  The goal of this paper is to furnish a literature on Goodwillie calculus for
functors defined between categories which derive from chain complexes over a
ground field $\Bbbk.$
  We characterize homogeneous functors $F: \mathcal{C} \longrightarrow
\mathcal{D}$ where $\mathcal{C} ,\mathcal{D}= Ch$ (chain complexes),
$Ch_+$(non-negatively graded chain complexes) or $\text{Alg}_\mathcal{O}$
(algebras over a chain complex operad $\mathcal{O}$). In the particular case
when $\mathcal{D}= \text{Alg}_\mathcal{O},$ our characterization requires
$\Bbbk$ to be of characteristics $0.$
  We are then extending the results of Walter \cite{Walt06} who studied in
characteristics $0$ the chain complex cases and when $\mathcal{O}$ is the Lie
operad.
