Permutads via operadic categories, and the hidden associahedron

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524776" target="_blank" >RIV/67985840:_____/20:00524776 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jcta.2020.105277" target="_blank" >https://doi.org/10.1016/j.jcta.2020.105277</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcta.2020.105277" target="_blank" >10.1016/j.jcta.2020.105277</a>

Result language
angličtina
Original language name
Permutads via operadic categories, and the hidden associahedron
Original language description
The present article exploits the fact that permutads (aka shuffle algebras) are algebras over a terminal operad in a certain operadic category Per. In the first, classical part we formulate and prove a claim envisaged by Loday and Ronco that the cellular chains of the permutohedra form the minimal model of the terminal permutad which is moreover, in the sense we define, self-dual and Koszul. In the second part we study Koszulity of Per-operads. Among other things we prove that the terminal Per-operad is Koszul self-dual. We then describe strongly homotopy permutads as algebras of its minimal model. Our paper shall advertise analogous future results valid in general operadic categories, and the prominent rôle of operadic (op)fibrations in the related theory.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-07776S" target="_blank" >GA18-07776S: Higher structures in algebra, geometry and mathematical physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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