On the pullback stability of a quotient map with respect to a closure operator
by
Lurdes Sousa
Escola Superior de Tecnologia do Instituto Politecnico de Viseu

Given a category equipped with a Dikranjan-Giuli closure operator c, the pullback stability of a c-quotient along some special morphisms is established. In particular, it is shown that, under mild conditions, the hereditary c-quotients are just the c-final morphisms; this generalizes a well-known result on topological spaces, since c-final for c the Kuratowski closure operator means pseudo-open. The universal c-quotients, that is, the c-quotients preserved by pullbacks along arbitrary morphisms, are also studied.

Date received: May 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-33.