  We introduce the notion of quasi-Ehresmann-Dedecker universes in quasi-set
theory in order to get a framework to develop a categorical version of
quasi-set theory, so characterizing the category Qset in a similar way as the
category Set is obtained from (say) ZFC plus universes. The Ehresmann-Dedecker
universes generalize the usual Sonner-Grothendieck universes and are more
adequate for dealing with Urelemente, which is the case of quasi-set theory.
This paper is just a sketch where the main ideas are presented.
