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We investigate the observationally-induced free algebra approach for constructing computational monads in the categories of classical domain theory. Our investigation yields that the free algebra construction exists for all finitary algebraic signatures and computational prototypes. We furthermore investigate the classical powerdomain constructions in the observationally-induced approach. For the Hoare, Smyth and probabilistic powerdomain constructions we build on established results, showingdoi:10.1016/j.entcs.2014.01.003 fatcat:tafw7qgpubab7n2767pco6lmqe