A-infinity-bimodules and Serre A-infinity-functors
| dc.creator | Lyubashenko, Volodymyr | |
| dc.creator | Manzyuk, Oleksandr | |
| dc.date | 2007-01-05 | |
| dc.date | 2008-02-15 | |
| dc.date.accessioned | 2026-07-07T09:20:51Z | |
| dc.date.available | 2026-07-07T09:20:51Z | |
| dc.description | We define A-infinity-bimodules similarly to Tradler and show that this notion is equivalent to an A-infinity-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative ring. Serre A-infinity-functors are defined via A-infinity-bimodules likewise Kontsevich and Soibelman. We prove that a unital closed under shifts A-infinity-category A over a field k admits a Serre A-infinity-functor if and only if its homotopy category H^0(A) admits a Serre k-linear functor. The proof uses categories enriched in K, the homotopy category of complexes of k-modules, and Serre K-functors. Also we use a new A-infinity-version of the Yoneda Lemma generalizing the previously obtained result. | |
| dc.description | 122 pages, Latex + Paul Taylor's diagrams.sty. This is the published version + complete proof of A-infinity Yoneda Lemma | |
| dc.identifier | https://arxiv.org/abs/math/0701165 | |
| dc.identifier | http://arxiv.org/abs/math/0701165 | |
| dc.identifier | Geometry and Dynamics of Groups and Spaces, Progress in Math., 265, Birkhauser, Basel (2007) 565-645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154853 | |
| dc.subject | Category Theory | |
| dc.title | A-infinity-bimodules and Serre A-infinity-functors | |
| dc.type | text |