Absolutely closed objects in a category
by
David Holgate
University of Stellenbosch
Coauthors: Gabriele Castellini (University of Puerto Rico)

Let X be a category with an (E, M) factorisation structure for sinks. An object X in X is absolutely c-closed for a closure operator c on X with respect to M iff every M-morphism with domain X is c-closed.

This sets up a Galois connection between the collection of all closure operators on X with respect to M (ordered pointwise) and all full subcategories of X (ordered by inclusion).

We study this Galois connection, and some of its restrictions which include the classical correspondence between closure operators and separated objects. The analogous case for ``absolutely dense objects" is also investigated.

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-30.