Geodesic
Homotopy theory of symmetric powers
Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 359-397.

Voir la notice de l'article provenant de la source International Press of Boston

We introduce the symmetricity notions of symmetric $h$-monoidality, symmetroidality, and symmetric flatness. As shown in our paper “Admissibility and rectification of colored symmetric operads” [PS14a], these properties lie at the heart of the homotopy theory of colored symmetric operads and their algebras. In particular, the former property can be seen as the analog of Schwede and Shipley’s monoid axiom for algebras over symmetric operads and allows one to equip categories of such algebras with model structures, whereas the latter ensures that weak equivalences of operads induce Quillen equivalences of categories of algebras. We discuss these properties for elementary model categories such as simplicial sets, simplicial presheaves, and chain complexes. Moreover, we provide powerful tools to promote these properties from such basic model categories to more involved ones, such as the stable model structure on symmetric spectra. This paper is also available at arXiv:1510.04969v3.
DOI : 10.4310/HHA.2018.v20.n1.a20
Classification : 18D50, 55P48, 18D20, 18G55, 55P43, 55U35
Keywords: model category, operad, symmetric power, symmetric flatness, symmetric $h$-monoidality, $D$-module 
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     title = {Homotopy theory of symmetric powers},
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Dmitri Pavlov; Jakob Scholbach. Homotopy theory of symmetric powers. Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 359-397. doi : 10.4310/HHA.2018.v20.n1.a20. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a20/

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