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On categories of ordered sets with a closure operator
by
Josef Slapal
Brno University of Technology
We define and study two categories of partially ordered sets endowed with a closure operator. The first category has order-preserving continuous maps as morphisms and it is shown to be concretely isomorphic to a category of ordered sets endowed with a compatible preorder. The second category studied has closed maps as morphisms and it is proved to be cartesian closed. As examples, consequences of these results for categories of the usual closure spaces and, in particular, of topological spaces are discussed.
Date received: May 21, 2008
Copyright © 2008 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 # caxi-05.