Harpaz, Yonatan and Nuiten, Joost and Prasma, Matan (2019) THE TANGENT BUNDLE OF A MODEL CATEGORY. THEORY AND APPLICATIONS OF CATEGORIES, 34. pp. 1039-1072. ISSN 1201-561X,
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This paper studies the homotopy theory of parametrized spectrum objects in a model category from a global point of view. More precisely, for a model category M satisfying suitable conditions, we construct a map of model categories TM -> M, called the tangent bundle, whose fiber over an object in M is a model category for spectra in its over-category. We show that the tangent bundle is a relative model category and presents the infinity-categorical tangent bundle, as constructed by Lurie. Moreover, the tangent bundle TM inherits an enriched model structure from M. This additional structure is used in subsequent work to identify the tangent bundles of algebras over an operad and of enriched categories, but may be of independent interest.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRA; Tangent category; model category; model fibration; spectrum |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Alexander Schmidt |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Apr 2020 09:08 |
| Last Modified: | 27 Apr 2020 09:08 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27753 |
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