The André–Quillen cohomology of commutative monoids
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Author(s)
Agrawalla, Bhavya
Khlaif, Nasief
Miller, Haynes
Date Issued
April 9, 2024
Journal
Semigroup Forum
Publisher
Springer US
Citation
Agrawalla, B., Khlaif, N. & Miller, H. The André–Quillen cohomology of commutative monoids. Semigroup Forum 108, 275–299 (2024).
Version
Author's final manuscript
Abstract
We observe that Beck modules for a commutative monoid are exactly modules over a graded commutative ring associated to the monoid. Under this identification, the Quillen cohomology of commutative monoids is a special case of the André–Quillen cohomology for graded commutative rings, generalizing a result of Kurdiani and Pirashvili. To verify this we develop the necessary grading formalism. The partial cochain complex developed by Pierre Grillet for computing Quillen cohomology appears as the start of a modification of the Harrison cochain complex suggested by Michael Barr.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1007/s00233-024-10423-z
