Goodwillie calculus in the category of algebras over a chain complex operad

Abstract

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 $\mathbb{k}.$ We characterize homogeneous functors $F:\mathcal{C}⟶\mathcal{D}$ where $\mathcal{C},\mathcal{D}=Ch$ (chain complexes), $C{h}_{+}$(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 $\mathbb{k}$ 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.

References in corpus (2)

• Homotopy theory of complete Lie algebras and Lie models of simplicial sets
• Rational Homotopy Calculus of Functors