A characterization of the category Q-TOP

Solovyov introduced in 2008 the notion of a Q-topological space (and Q-continuous maps between them), where Q is a fixed member of a variety of Ω -algebras, which in turn gives rise to the category Q-TOP of such spaces. The purpose of this note is to give a characterization of this category (in a large class of categories), in terms of a "Sierpinski-like" object, which is similar to the one given by Manes in 1974 for the category TOP of topological spaces.