The authors present a categorical generalization of a well-known result in model theory, the Fraisse-Jonsson theorem, by which they characterize large classes of reasonable categories if they contain universal homogeneous objects. As a first application, they derive from this, for various categories of bifinite domains and with embedding-projection pairs as morphisms, the existence and uniqueness of universal homogeneous objects, and they deduce C.A. Gunter and A. Jung's result (see Logic in Computer Science, Comput. Sci. Press, p.309-19 (1988)) from this. Various categories of stable bifinite domains which apparently have not been considered in the literature before are introduced, and universal homogeneous objects for these categories (with stable embedding-projection pairs) are obtained. For four categories of even domains it is shown that although these categories contain universal objects they do not contain universal homogeneous objects. Finally, it is shown that all the constructions can be performed effectively.
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