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

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dc.creatorBrown, R.
dc.creatorKamps, H. K.
dc.creatorPorter, T.
dc.date2004-10-18
dc.date.accessioned2026-07-07T05:13:23Z
dc.date.available2026-07-07T05:13:23Z
dc.descriptionThis 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.
dc.description19 pages, uses pictex
dc.identifierhttps://arxiv.org/abs/math/0410398
dc.identifierhttp://arxiv.org/abs/math/0410398
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72925
dc.subjectAlgebraic Topology
dc.subjectCategory Theory
dc.subject18D05,20L05,55Q05, 55Q35
dc.titleA homotopy double groupoid of a Hausdorff space II: a van Kampen theorem
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