Groupoid preactions by partial homeomorphisms and homogenizations
by
Michael Megrelishvili
Bar-Ilan University, Israel

We prove that for every groupoid of partial homeomorphisms on a topological space X there exists a topological embedding X -> Y and a universal group action on the space Y which extends the given groupoid action. We apply this method for homogenizations of topological spaces (preserving several topological properties). The acting group is just the universal group U(P) over the groupoid P. This construction can be described in terms of Kan extension. Justifying once again the principle of " expressing everything as Kan extension". We discuss also some possible generalizations for several categories as well as the case of topological groupoids.

email:megereli@macs.biu.ac.il

http://www.cs.biu.ac.il/~megereli/groupoid.html

Date received: May 25, 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-14.