The André-Quillen cohomology of commutative monoids
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913375495127040 |
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| author | Agrawalla, Bhavya Khlaif, Nasief Miller, Haynes |
| author_facet | Agrawalla, Bhavya Khlaif, Nasief Miller, Haynes |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01536 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The André-Quillen cohomology of commutative monoids Agrawalla, Bhavya Khlaif, Nasief Miller, Haynes Rings and Algebras Commutative Algebra 20M14, 13D03 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 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. |
| title | The André-Quillen cohomology of commutative monoids |
| topic | Rings and Algebras Commutative Algebra 20M14, 13D03 |
| url | https://arxiv.org/abs/2211.01536 |