We consider the category-theoretic structure of abstract elementary classes (AECs), and consider their relationship to accessible categories, the latter being category theorists' proposed context in which to analyze classes of models (elementary or otherwise). We translate a few notions and techniques related to accessible categories into the realm of AECs, and draw two surprising conclusions. Building on work described in the previous talk, we discover that the connection with accessible categories yields a partial Galois stability spectrum result for weakly tame AECs. Moreover, using nothing more than the Yoneda embedding, we obtain a peculiar structure theorem for categorical AECs, where the models may be replaced by sets equipped with actions of the monoid of endomorphisms of the categorical structure. These results--clear at the level of category theory, but unforeseeable from other angles--illustrate the potent role that this perspective may yet play in model theory.