A universal characterization of the curved homotopy Lie and associative operads
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912423440547840 |
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| author | Laplante-Anfossi, Guillaume Petr, Adrian Shende, Vivek |
| author_facet | Laplante-Anfossi, Guillaume Petr, Adrian Shende, Vivek |
| contents | We study the category of nonsymmetric dg operads valued in strict graded-mixed complexes, equipped with a distinguished arity zero weight one element which generates the weight grading, and whose differential has weight one. We show that the initial object is the curved A-infinity operad, that the forgetful functor to the category of operads under it admits a right adjoint, and that the unit of the adjunction encodes the operation of twisting a curved A-infinity algebra by a Maurer-Cartan element.
The corresponding notions for symmetric operads characterize the curved L-infinity operad and the corresponding twisting procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A universal characterization of the curved homotopy Lie and associative operads Laplante-Anfossi, Guillaume Petr, Adrian Shende, Vivek Algebraic Topology Category Theory Symplectic Geometry 18M70 We study the category of nonsymmetric dg operads valued in strict graded-mixed complexes, equipped with a distinguished arity zero weight one element which generates the weight grading, and whose differential has weight one. We show that the initial object is the curved A-infinity operad, that the forgetful functor to the category of operads under it admits a right adjoint, and that the unit of the adjunction encodes the operation of twisting a curved A-infinity algebra by a Maurer-Cartan element. The corresponding notions for symmetric operads characterize the curved L-infinity operad and the corresponding twisting procedure. |
| title | A universal characterization of the curved homotopy Lie and associative operads |
| topic | Algebraic Topology Category Theory Symplectic Geometry 18M70 |
| url | https://arxiv.org/abs/2412.14851 |