Operadic structure on the Gerstenhaber-Schack complex for prestacks
| Autor: | Van, Hoang Dinh, Hermans, Lander, Lowen, Wendy |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Selecta Mathematica New Series 28, article no. 47 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00029-022-00759-1 |
| Popis: | We introduce an operad which acts on the Gerstenhaber-Schack complex of a prestack as defined by Dinh Van and Lowen, and which in particular allows us to endow this complex with an underlying $L_{\infty}$-structure. We make use of the operad $\operatorname{Quilt}$ which was used by Hawkins in order to solve the presheaf case. Due to the additional difficulty posed by the presence of twists, we have to use $\operatorname{Quilt}$ in a fundamentally different way (even for presheaves) in order to allow for an extension to prestacks. The resulting $L_{\infty}$-algebra governs the deformation theory of the prestack. Comment: 38 pages, To appear in Selecta Math. Corrected typos, added 45 explanatory drawings, revised notations and provided more explicit definitions and explanations, referred section 2.4 to the appendix and replaced it with a generators and relations description, corrected lemma 2.24, the following definitions, constructions and examples are new: 2.5, 2.6, 2.19, 2.22, 2.29, 3.1, 3.19, 3.25, 4.7 |
| Databáze: | arXiv |
| Externí odkaz: |
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