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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Model structures for coalgebras
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by Gabriel C. Drummond-Cole and Joseph Hirsh PDF
Proc. Amer. Math. Soc. 144 (2016), 1467-1481 Request permission

Abstract:

Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphism on homology. In the other, the weak equivalences are maps which induce a weak equivalence of algebras under the cobar functor. We unify these two approaches, realizing them as the two extremes of a partially ordered set of model category structures on coalgebras over a cooperad satisfying mild conditions.
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Additional Information
  • Gabriel C. Drummond-Cole
  • Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Republic of Korea 37673
  • Email: gabriel@ibs.re.kr
  • Joseph Hirsh
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139
  • MR Author ID: 999293
  • Received by editor(s): November 20, 2104
  • Received by editor(s) in revised form: April 4, 2015, and April 22, 2015
  • Published electronically: October 8, 2015
  • Additional Notes: This work was supported by IBS-R003-D1
    The second author was supported by NSF DMS-1304169.
  • Communicated by: Michael A. Mandell
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 1467-1481
  • MSC (2010): Primary 18D50, 55U30
  • DOI: https://doi.org/10.1090/proc/12823
  • MathSciNet review: 3451225