Speaker
Description
We establish a technical framework that includes a bicategory of enhanced triangulated categories with certain enhanceable functors and natural transformations, and a theory of A-infinity algebra and module objects in this setting. This allows us to prove the analogue of the Barr-Beck theorem for enhanced triangulated categories. Moreover, we provide a DG category whose derived category of modules is equivalent to our analogue of the Eilenberg-Moore category of the monad RF, where (F,R) are adjoint enhanced functors between enhanced triangulated categories. We also develop a notion of the derived category of comodules over an A-infinity coalgebra satisfying some restrictions in our formalism, equipped with module-comodule correspondence, and stable under coalgebra homotopy equivalences. Together, this implies a version of descent for derived categories of sheaves. This is joint work with Timothy Logvinenko.
