The Andr\'e-Quillen cohomology of commutative monoids
Rings and Algebras
2024-06-05 v5 Commutative Algebra
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 Andr\'e-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.
Keywords
Cite
@article{arxiv.2211.01536,
title = {The Andr\'e-Quillen cohomology of commutative monoids},
author = {Bhavya Agrawalla and Nasief Khlaif and Haynes Miller},
journal= {arXiv preprint arXiv:2211.01536},
year = {2024}
}
Comments
Extensive revision of an earlier arXiv submission, with new title. This is the published version with different pagination