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24 p, 2002, Theory and Applications of Categories, Vol. 10, No. 2, 2002, pp. 71--93.

Abstract:

From authors' Abstract: the aim of the paper is to ``associate to a Hausdorff space, X, a double groupoid, ρ2 (X), the homotopy double groupoid of X. The construction is based on the geometric notion of thin square. Under the equivalence of categories between small 2--categories and double categories with connection given in [BM] the homotopy double groupoid corresponds to the homotopy 2--groupoid, G2(X), constructed in [HKK]. The cubical nature of ρ2 (X) as opposed to the globular nature of G2(X) should provide a convenient tool when handling `local-to-global' problems as encountered in a generalised van Kampen theorem and dealing with tensor products and enrichments of the category of compactly generated Hausdorff spaces." in: Theory and Applications of Categories, Vol. 10, No. 2, 2002, pp. 71--93.

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http://www.tac.mta.ca/tac/volumes/10/2/10-02.pdf

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HomotopyDG2k2.pdf

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