|
|||||
 |
|
|
|
Generalized stability for
abstract homotopy theories
Moritz Rahn and Michael Shulman |
|
Vol. 6 (2021), No. 1, 1–28
|
|
DOI: 10.2140/akt.2021.6.1
|
Abstract |
|
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. |
PDF Access Denied
We have not been able to recognize your IP address
18.188.61.223
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
derivator, stable derivator, stable $\infty$-category,
absolute colimit
|
Mathematical Subject Classification 2010
Primary: 55U35
|
Milestones
Received: 29 April 2019
Revised: 29 July 2020
Accepted: 17 October 2020
Published: 8 July 2021
|
Authors |
| Moritz Rahn | |
| Mathematisches Institut Johannes Gutenberg-Universität Mainz Germany |
|
| Michael Shulman | |
| Department of Mathematics University of San Diego San Diego, CA United States |
|
