Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization

We study the classification problem of simple transitive 2 -representations of the 2-category of finite-dimensional bi-modules over a radical square zero Nakayama algebra. This results in a complete classification of simple transitive 2 -representations whose apex is a finitary two-sided cell. We define a notion of localization of 2-representations. We con-struct previously unknown simple transitive 2-representations as localizations of cell 2-representations. Using the universal property of our construction we prove that any simple tran-sitive 2-representation with finitary apex is equivalent to a localization of a cell 2-representation.