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We devise a fairly general sufficient condition ensuring that theendomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. aFra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach providesus not only with a framework unifying the previous scattered results in thisvein, but actually yields new applications for endomorphism monoids of the(rational) Urysohn space and the countable universal ultrahomogeneoussemilattice.

A universality result for endomorphism monoids of some ultrahomogeneous structures