`Double modules', double categories and groupoids, and a new homotopical double groupoid

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We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting of a space, two subspaces, and a set of base points, under a condition which also implies that this double groupoid contains two second relative homotopy groups.
7 pages, 1 figure, QED.sty v.2 This version explains and proves the relation of the homotopy double groupoid with two second relative homotopy groups. Also extra references added

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Category Theory, Algebraic Topology, 18B40; 18D05; 55E30

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http://salesiana.dossiersoluciones.com/handle/123456789/223961

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.2627
 http://arxiv.org/abs/0903.2627

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arXiv