In this paper we develop the combinatorics of leveled trees in order to construct explicit resolutions of (co)operads and (co)operadic (co)bimodules. We construct explicit cofibrant resolutions of operads and operadic bimodules in spectra analogous to the ordinary Boardman–Vogt resolutions and we express them as a cobar construction of indecomposable elements. Dually, in the context of CDGAs, we perform similar constructions to obtain fibrant resolutions of Hopf cooperads and Hopf cooperadic cobimodules and we express them as a bar construction of primitive elements.
Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules
- Author(s)
- Ricardo Campos, Julien Ducoulombier, Najib Idrissi.
- Publication
- In: High. Struct. 5.1, pp. 293–366 (2021), 74 pages.
- Online on
- Updated on
- Accepted on
- Full text
- https://cdn.idrissi.eu/main/research/bar-cobar.pdf
- DOI:10.21136/HS.2021.09
- https://doi.org/10.21136/HS.2021.09
- arXiv:1911.09474
- https://arxiv.org/abs/1911.09474
- hal-01786218
- https://hal.science/hal-01786218
- MR4367224
- https://mathscinet.ams.org/mathscinet/article?mr=4367224
- Zbl 7482172
- https://zbMath.org/?q=an:7482172