Title: Cellular dg-categories and their applications to homotopy theory of A-infinity categories
Description: We introduce the notion of cellular dg-categories mimicking the properties of topological CW-complexes. We study the properties of such categories and provide various examples corresponding to the well-known geometrical objects. We also show that these categories are suitable for encoding coherence conditions in homotopy theoretical constructs involving A-infinity categories. In particular, we formulate the notion of a homotopy coherent monoid action on an A-infinity category which can be used in constructions involved in Homological Mirror Symmetry.