#
A homotopy double groupoid of a Hausdorff
space II: a van Kampen theorem

##
R. Brown, K.H. Kamps, and T. Porter

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.

Keywords:
double groupoid, double category, thin structure, connections,
commutative cube, van Kampen theorem

2000 MSC:
18D05, 20L05, 55Q05, 55Q35

*Theory and Applications of Categories,*
Vol. 14, 2005,
No. 9, pp 200-220.

http://www.tac.mta.ca/tac/volumes/14/9/14-09.dvi

http://www.tac.mta.ca/tac/volumes/14/9/14-09.ps

http://www.tac.mta.ca/tac/volumes/14/9/14-09.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/9/14-09.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/9/14-09.ps

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