Subject: categories: preprint: A van Kampen theorem for the homotopy double groupoid of a Hausdorff space

From: Ronnie Brown <[email-masked]>
Date: Thu, 15 Jan 2004 17:00:59 +0000

Preprint available

http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/04/algtop04.html#04.01

04.01 : BROWN, R., KAMPS, K.H. & PORTER, T.

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

Summary:

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.

Ronnie Brown

 Professor Emeritus R. Brown,
 Department of Mathematics,
 University of Wales, Bangor
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