The following could be of interest to some on the category theory bulletin, since this gives explicit computation of certain finite crossed modules and so of specific kinds of double groupoids, ... Best wishes, Ronnie ---------- Forwarded message ---------- Date: Sat, 18 Jan 97 16:25:41 +0000 (GMT) From: Derek Holt <dfh@maths.warwick.ac.uk> To: Multiple recipients of list <GAP-Forum@Math.RWTH-Aachen.DE> Subject: New share package for crossed modules A new GAP share package written by Chris Wensley and Murat Alp, for calculating in crossed modules and cat1 groups is now available, and can be collected from the GAP incoming directory in the file xmod131.tar.gz. The GAP web page description is included below. Derek Holt. ****************************************************************************** XMod Authors: Chris Wensley, Murat Alp Language: GAP Operating System: Any Available from: http://www.math.rwth-aachen.de/ftp/pub/incoming/xmod131.tar.gz, Description This package enables construction of and computation with objects within the equivalent categories of crossed modules and cat1-groups, where the groups involved are finite of moderately small order. A crossed module consists of two groups S and R, together with a homomorphism from S to R which essentially commutes with conjugation within S and R. Functions are provided for each of the standard constructions of crossed modules, and for computing with sub- and quotient-structures and homomorphisms. A cat1-group consists of a group G together with two homomorphisms from G to G satisfying certain conditions. It was shown by Loday that there is a natural one-one correspondence between cat1-groups and crossed modules. An important notion is a derivation of a crossed module, which is a map from R to S satisfying certain conditions. It is possible to compute all (or all regular) derivations of a crossed module. There are also functions for computing the actor of a crossed module X, which is a crossed module whose range is the automorphism group of X. Authors Chris Wensley and Murat Alp School of Mathematics University of Wales, Bangor Gwynedd, LL57 1UT GB email: c.d.wensley@bangor.ac.uk ~e