Operadic right modules via the dendroidal formalism

2024/09/02 by Barata, Miguel
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.01188

Abstract

In this work we study the homotopy theory of the category RMod_P of right modules over a simplicial operad P via the formalism of forest spaces fSpaces, as introduced by Heuts, Hinich and Moerdijk. In particular, we show that, for P is closed and Σ-free, there exists a Quillen equivalence between the projective model structure on RMod_P, and the contravariant model structure on the slice category fSpaces_/NP over the dendroidal nerve of P. As an application, we comment on how this result can be used to compute derived mapping spaces of between operadic right modules.

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