A note describing A CATEGORICAL SETTING FOR THE 4-COLOUR THEOREM by Dusko Pavlovic is available by anonymous ftp. Abstract: It is well known that the 4-colouring of maps is equivalent to the 3-colouring of the edges of some graphs. We show that every slice of the category of 3-coloured graphs is a topos. The forgetful functor to the category of graphs is cotripleable; every loop-free graph is covered by a 3-coloured one in a universal way. In this context, the 4-Color Theorem becomes a statement about the existence of coalgebra structure on graphs. The "projective" approach to graphs, described here, is, in a sense, dual to the usual combinatorial treatment, based on induction. I shall try to relate the two approaches in another paper. How to get a copy:

ftp triples.math.mcgill.ca login: anonymous password:[your e-mail address] cd pub/pavlovic bin get 4color-US.ps.Z %if your printer has American standards %or get 4color-A4.ps.Z %otherwise bye uncompress 4color-++.ps.Z

If you have any problems printing out this PS-file, please let me know. (I am not distributing the DVI or LaTeX versions of the paper because it contains several PS-diagrams.) Regards, Dusko ==============================================================================