Geodesic
A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem
Theory and applications of categories, Tome 14 (2005), pp. 200-220.

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This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 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. An integral part of the proof 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. These results have recently been generalised to all dimensions by Philip Higgins.
Classification : 18D05, 20L05, 55Q05, 55Q35
Keywords: double groupoid, double category, thin structure, connections, commutative cube, van Kampen theorem 
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     author = {R. Brown and K.H. Kamps and T. Porter},
     title = {A homotopy double groupoid of a {Hausdorff
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     url = {http://geodesic.mathdoc.fr/item/TAC_2005_14_a8/}
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R. Brown; K.H. Kamps; T. Porter. A homotopy double groupoid of a Hausdorff
space II:  a van Kampen theorem. Theory and applications of categories, Tome 14 (2005), pp. 200-220. http://geodesic.mathdoc.fr/item/TAC_2005_14_a8/