|Speaker:||Giovanni Faonte (Yale University)|
|Title:||Nerve construction, A-infinity functors and homotopy theory of dg-categories|
|Date (JST):||Thu, Dec 11, 2014, 15:30 - 17:00|
|Place:||Seminar Room A|
In this talk we show how to obtained Toen's derived enrichment of the model category of dg-categories defined by Tabuada using by the dg-category of A-infinity functors. This approach was suggested by Kontsevich. We further put this construction into the framework of (infinity,2)-categories. Namely, we show that the categories of dg and A-infinity categories can be enhanced to (infinity,2)-categories. The enhancement is defined using the nerve construction for A-infinity categories, which generalizes the dg-nerve of Lurie. We prove that the (infinity,1)-truncation of to the (infinity,2)-category of dg-categories is a model for the simplicial localization at the model structure of Tabuada. As an application, we prove that the homotopy groups of the mapping space of endomorphisms at the identity functor in the (infinity,2)-category of A-infinity categories compute the Hochschild cohomology.
G. Faonte, A-infinity functors and homotopy theory of dg-categories, arXiv:1412.1255.
G. Faonte, Simplicial nerve of an A-infinity category, arXiv:1312.2127.