Harpaz, Yonatan and Nuiten, Joost and Prasma, Matan (2019) Tangent categories of algebras over operads. ISRAEL JOURNAL OF MATHEMATICS, 234 (2). pp. 691-742. ISSN 0021-2172, 1565-8511
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Associated to a presentable infinity-category nd an object X is an element of C is the tangent infinity-category TXC, consisting of parameterized spectrum objects over X. This gives rise to a cohomology theory, called Quillen cohomology, whose category of coefficients is TXC. When consists of algebras over a nice infinity-operad in a stable infinity-category, is equivalent to the infinity-category of operadic modules, by work of Basterra-Mandell, Schwede and Lurie. In this paper we develop the model-categorical counterpart of this identification and extend it to the case of algebras over an enriched operad, taking values in a model category which is not necessarily stable. This extended comparison can be used, for example, to identify the cotangent complex of enriched categories, an application we take up in a subsequent paper.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HOMOTOPY-THEORY; MODEL; LOCALIZATION; COHOMOLOGY; SPECTRA; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Mar 2020 05:46 |
| Last Modified: | 06 Apr 2020 06:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26020 |
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