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Generalized stability for
abstract homotopy theories
Moritz Rahn and Michael Shulman |
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Vol. 6 (2021), No. 1, 1–28
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DOI: 10.2140/akt.2021.6.1
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Abstract |
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We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, if and only if homotopy finite limit functors have right adjoints, and if and only if homotopy finite colimit functors have left adjoints. These characterizations generalize to an abstract notion of “stability relative to a class of functors”, which includes in particular pointedness, semiadditivity, and ordinary stability. To prove them, we develop the theory of derivators enriched over monoidal left derivators and weighted homotopy limits and colimits therein. |
Keywords
derivator, stable derivator, stable $\infty$-category,
absolute colimit
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Mathematical Subject Classification 2010
Primary: 55U35
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Milestones
Received: 29 April 2019
Revised: 29 July 2020
Accepted: 17 October 2020
Published: 8 July 2021
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Authors |
| Moritz Rahn | |
| Mathematisches Institut Johannes Gutenberg-Universität Mainz Germany |
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| Michael Shulman | |
| Department of Mathematics University of San Diego San Diego, CA United States |
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