Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic 
(co)bimodules

Campos, Ricardo; Ducoulombier, Julien; Idrissi, Najib

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Journal Article

Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules

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Ducoulombier, Julien
Max Planck Institute for Mathematics, Max Planck Society;

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https://higher-structures.math.cas.cz/api/files/issues/Vol5Iss1/CamIdrduc
(Publisher version)

https://doi.org/10.48550/arXiv.1911.09474
(Preprint)

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Campos-Ducoulombier-Idrissi_Boardman-Vogt resolutions_2021.pdf
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Citation

Campos, R., Ducoulombier, J., & Idrissi, N. (2021). Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules. Higher Structures, 5(1), 310-383.

Cite as: https://hdl.handle.net/21.11116/0000-0009-F0A5-D

Abstract

We develop the combinatorics of leveled trees in order to construct explicit
resolutions of (co)operads and (co)operadic (co)bimodules. We build explicit
cofibrant resolutions of operads and operadic bimodules in spectra analogous to
the ordinary Boardman--Vogt resolutions and we express them as cobar
constructions of indecomposable elements. Dually, in the context of CDGAs, we
perform similar constructions, and we obtain fibrant resolutions of Hopf
cooperads and Hopf cooperadic cobimodules. We also express them as bar
constructions of primitive elements.