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Mathematics Preprints 2009

Algebraic Topology

09.01 : BROWN, R.

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

Summary:

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.

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