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Model structures for coalgebras


Authors: Gabriel C. Drummond-Cole and Joseph Hirsh
Journal: Proc. Amer. Math. Soc. 144 (2016), 1467-1481
MSC (2010): Primary 18D50, 55U30
DOI: https://doi.org/10.1090/proc/12823
Published electronically: October 8, 2015
MathSciNet review: 3451225
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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

DOI: https://doi.org/10.1090/proc/12823
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
Article copyright: © Copyright 2015 American Mathematical Society