Crossed modules and cohomology of algebras over an operad
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909481772777472 |
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| author | Leray, Johan Rivière, Salim Wagemann, Friedrich |
| author_facet | Leray, Johan Rivière, Salim Wagemann, Friedrich |
| contents | We introduce a general definition of a $n$-crossed module of $P$-algebras over an algebraic operad $P$, which coincides with historical definitions in the cases of the operads As and Lie and $n = 1$. We establish a natural isomorphism between the abelian group of equivalence classes of $n$-crossed modules over a pair $(A,M)$ for an operad $P$ and the $(n+1)^\text{th}$ operadic cohomology group of $A$ with coefficients in $M$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_04614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crossed modules and cohomology of algebras over an operad Leray, Johan Rivière, Salim Wagemann, Friedrich K-Theory and Homology Algebraic Topology Category Theory 18D35, 18D50, 18G55 We introduce a general definition of a $n$-crossed module of $P$-algebras over an algebraic operad $P$, which coincides with historical definitions in the cases of the operads As and Lie and $n = 1$. We establish a natural isomorphism between the abelian group of equivalence classes of $n$-crossed modules over a pair $(A,M)$ for an operad $P$ and the $(n+1)^\text{th}$ operadic cohomology group of $A$ with coefficients in $M$. |
| title | Crossed modules and cohomology of algebras over an operad |
| topic | K-Theory and Homology Algebraic Topology Category Theory 18D35, 18D50, 18G55 |
| url | https://arxiv.org/abs/2411.04614 |