Fraïssé limits in comma categories
This paper uses the Droste-Göbel categorical formulation of Fraïssé's theorem to produce sufficient conditions for a comma category to contain a universal homogeneous object [\textit{M. Droste} and \textit{R. Göbel}, Contemp. Math. 131, 49--74 (1992; Zbl 0759.18002)]. The main theorem is expressed in terms of 10 properties, so will not be reproduced here. Using the criterion of this theorem, the paper characterizes homogeneous structures which possess universal homogeneous endomorphisms. Finally, the paper characterizes the retracts of homogeneous structures that are induced by universal homogeneous retractions. For example, every retract of any of the following structures is induced by a universal homogeneous retraction: the countable random graph, the countable atomless Boolean algebra, the countable dense linear order, the countable generic poset, and the rational Urysohn space.
scientific article; zbMATH DE number 6916419
scientific article