Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908477875552256 |
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| author | Balodi, Mamta Banerjee, Abhishek Kour, Surjeet |
| author_facet | Balodi, Mamta Banerjee, Abhishek Kour, Surjeet |
| contents | We obtain Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients in half-braidings for a monoidal functor. Our approach uses a formal analogy between half-braidings of a monoidal functor and the entwining of a coalgebra with an algebra. We show that the Davydov-Yetter complex with coefficients carries the structure of a weak comp algebra. In particular, it is equipped with two distinct cup product structures $\cup$ and $\sqcup$ which are related in a manner that replaces graded commutativity. We also introduce a subcomplex of the Davydov-Yetter complex with coefficients whose cohomology forms a Gerstenhaber algebra in the usual sense. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients Balodi, Mamta Banerjee, Abhishek Kour, Surjeet Category Theory Rings and Algebras 18M05, 16E40 We obtain Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients in half-braidings for a monoidal functor. Our approach uses a formal analogy between half-braidings of a monoidal functor and the entwining of a coalgebra with an algebra. We show that the Davydov-Yetter complex with coefficients carries the structure of a weak comp algebra. In particular, it is equipped with two distinct cup product structures $\cup$ and $\sqcup$ which are related in a manner that replaces graded commutativity. We also introduce a subcomplex of the Davydov-Yetter complex with coefficients whose cohomology forms a Gerstenhaber algebra in the usual sense. |
| title | Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients |
| topic | Category Theory Rings and Algebras 18M05, 16E40 |
| url | https://arxiv.org/abs/2508.02285 |