Quasi-Eheresmann-Dedecker Universes

TL;DR

This paper introduces quasi-Ehresmann-Dedecker universes within quasi-set theory to develop a categorical framework analogous to set theory universes, accommodating Urelemente for quasi-set theory.

Contribution

It proposes a new notion of universes tailored for quasi-set theory, enabling a categorical characterization similar to classical set theory universes.

Findings

Defines quasi-Ehresmann-Dedecker universes for quasi-set theory.

Provides a categorical framework for quasi-set theory.

Lays groundwork for further development of categorical quasi-set theory.

Abstract

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.