Pavlov, Dmitri and Scholbach, Jakob (2018) HOMOTOPY THEORY OF SYMMETRIC POWERS. HOMOLOGY HOMOTOPY AND APPLICATIONS, 20 (1). pp. 359-397. ISSN 1532-0073, 1532-0081
Full text not available from this repository.Abstract
We introduce the symmetricity notions of symmetric hmonoidality, symmetroidality, and symmetric flatness. As shown in our paper [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 ar Xiv:1510.04969v3.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SIMPLICIAL PRESHEAVES; MODEL CATEGORIES; SPECTRA; MODULES; model category; operad; symmetric power; symmetric flatness; symmetric h-monoidality; D-module |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Mar 2020 09:48 |
| Last Modified: | 20 Mar 2020 09:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15355 |
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