TITLE: Double modules', double categories and groupoids, and a new homotopical double groupoid

AUTHOR: Ronald Brown 

ABSTRACT: We give a rather general construction of double categories and so,
under further conditions, double groupoids,  from a structure we
call a `double module'.

We also give a homotopical construction of a double groupoid from a
triad consisting of a space, two subspaces, and a set of base
points, under a condition which also implies that this double
groupoid contains two second relative homotopy groups.

AUTHOR'S ADDRESS: School of Computer Science, Bangor University, Bangor, Gwynedd, LL57 1UT, UK

web site: www.bangor.ac.uk/r.brown 

AMSCLASSIFICATIO: 18B40,18D05,55E30 

KEYWORDS: double categories, double groupoids, crossed modules, second relative homotopy groups

arXiv: 0903.2627