We present fixed-point based characterization of several classes of co-observable languages that are of interest in the context of decentralized supervisory control of discrete-event systems, including CWP V DWA co-observable languages, CWP co-observable languages, and DWA co-observable languages. We also provide formulas for computing super/sublanguages for each of these classes. In cases where the class of co-observable languages is not closed under intersection/union, we provide upper/lower bound of the super/sublanguage formula we present. The computation of super/sublanguages and also computation of their upper/lower bounds has lead to the introduction of other classes of co-observable languages, namely, strongly CWP co-observable languages, strongly DWA co-observable languages, locally observable languages, and strongly locally observable languages. Fixed-point based characterization of all the above language classes is also given, and their closure under intersection/union is investigated. We also study whether the fixed-point operator preserves prefix closure, relative closure (also called L-m(G) -closure), and controllability.