TITLE: A van Kampen theorem for the homotopy double groupoid of a Hausdorff
space

AUTHORS: R. Brown, K.H. Kamps, T.Porter
EMAILS: r.brown@bangor.ac.uk, heiner.kamps@fernuni-hagen.de, t.porter@bangor.ac.uk
ADDRESSES: Mathematics Department, Dean St.,
Bangor, Gwynedd LL57 1UT, UK. , Fachbereich Mathematik, FernUniversit\"at in Hagen,
D-58084 Hagen, Germany., Mathematics Department, Dean St., Bangor, Gwynedd LL57 1UT, UK.

ABSTRACT: We show that the homotopy double groupoid of a Hausdorff space
defined by the authors in a previous paper satisfies a version of
the van Kampen theorem, and so is a suitable tool for non abelian,
2-dimensional,  local-to-global problems. The methods are
analogous to those developed  by Brown and Higgins for similar
theorems for other higher homotopy groupoids.

There is a detailed discussion of commutative cubes in a double
category with connections, and a proof of the key result that any
composition of commutative cubes is commutative.