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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Induced model structures for higher categories
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by Philip Hackney and Martina Rovelli PDF
Proc. Amer. Math. Soc. 150 (2022), 4629-4644


We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an application, we construct new model structures on cubical sets, prederivators, marked simplicial sets and simplicial spaces modeling $\infty$-categories and $\infty$-groupoids.
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Additional Information
  • Philip Hackney
  • Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
  • MR Author ID: 758568
  • ORCID: 0000-0001-8050-7431
  • Email:
  • Martina Rovelli
  • Affiliation: Department of Mathematics and Statistics, University of Massachusetts Amherst, Massachusetts 01003-9305
  • MR Author ID: 1204481
  • Email:
  • Received by editor(s): February 15, 2021
  • Received by editor(s) in revised form: January 5, 2022, and January 12, 2022
  • Published electronically: June 10, 2022
  • Additional Notes: This work was supported by the National Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2020 semester.
  • Communicated by: Julie Bergner
  • © Copyright 2022 by the authors
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 4629-4644
  • MSC (2020): Primary 18N60, 55U35, 18N40; Secondary 18A40, 18N50, 55U10
  • DOI:
  • MathSciNet review: 4489301