The well-known theorem that finite limits can be obtained via finite products and equalizers has as a corollary that finite limits can also be obtained via pullbacks and a terminal object. This also yields a decomposition of any limiting cone over some finite diagram into pullback squares, with possibly the terminal object insterted at some places. Obviously, from the above proof, one gets a rather clumsy decomposition, e.g. with many unecessary terminal objects inserted. Is there any "better" decomposition (whatever this means, but e.g. a multiple pullback of three arrows should be decomposed into three pullback squares, and not seven of them)? Till Mossakowski -- Till Mossakowski Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen till@tzi.de P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till 29-Mar-2002 15:14:54 -0400,1662;000000000000-00000000