Categories of the 4-valued inverse order nested sets

In this paper, the connection of the 4-valued inverse order nested sets and topos theory is considered. The category QNS of the 4-valued inverse order nested sets is constructed. It is shown that in the category QNS exist Equalizers, Finite Products, Terminal Objects, Exponentials and Subobject Classifiers. Consequently the category QNS forms a topos.