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

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

2009-03-15

arxiv.org/abs/0903.2627v2

Mathematics

Category Theory

7 pages, 1 figure, QED.sty v.2 This version explains and proves the relation of the homotopy double groupoid with two second r

Scientific paper

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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