Transfers of $A_\infty$- and other homotopy structures as Grothendieck bifibrations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912092190146560 |
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| author | Markl, Martin |
| author_facet | Markl, Martin |
| contents | We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then generalize our results to P-infinity structures over a field of characteristic zero, for any quadratic Koszul operad P. An immediate application is a categorical framework in which the transfers of e.g. A-infinity, L-infinity and C-infinity structures are strictly functorial. A by product of our reasoning is a general transfer theorem for P-infinity algebras, which we prove in the last section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transfers of $A_\infty$- and other homotopy structures as Grothendieck bifibrations Markl, Martin Algebraic Topology 16E99, 55S20 We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then generalize our results to P-infinity structures over a field of characteristic zero, for any quadratic Koszul operad P. An immediate application is a categorical framework in which the transfers of e.g. A-infinity, L-infinity and C-infinity structures are strictly functorial. A by product of our reasoning is a general transfer theorem for P-infinity algebras, which we prove in the last section. |
| title | Transfers of $A_\infty$- and other homotopy structures as Grothendieck bifibrations |
| topic | Algebraic Topology 16E99, 55S20 |
| url | https://arxiv.org/abs/2403.17526 |