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arXiv · 1904.13100

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

Miradain Atontsa Nguemo
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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 $\Bbbk.$ 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.

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Miradain Atontsa Nguemo. 2019-04-30. Goodwillie calculus in the category of algebras over a chain complex operad. https://arxiv.org/abs/1904.13100

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