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Miradain Atontsa Nguemo

Publications and source records attributed to Miradain Atontsa Nguemo.

2 recordsLinked to original sources

arXiv2019

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

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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arXiv2019

Equivalence of Operads over Symmetric Monoidal Categories

In this paper, we study conditions for extending Quillen model category properties , between two symmetric monoidal categories, to their associated category of symmetric sequences and of operads. Given a Quillen equivalence $λ: \mathcal{C}=Ch_{\Bbbk,t} \leftrightarrows \mathcal{D}: R,$ so that $\mathcal{D}$ is any symmetric monoidal category and the adjoint pair $(λ, R)$ is weak monoidal, we prove that the categories of connected operads $Op_\mathcal{C}$ and $Op_\mathcal{D}$ are Quillen equivalent. This expands an analogous result of Schwede-Shipley(\cite{SS03}) when we replace these categories of operads with the sub-categories of $\mathcal{C}$-Monoid and $\mathcal{D}$-monoid.

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