homotopy double groupoid of a Hausdorff space

Homotopy double groupoidPlanetmathPlanetmath of a Hausdorff space

Let X be a Hausdorff space. Also consider the HDA concept of a double groupoidPlanetmathPlanetmathPlanetmath (http://planetmath.org/HigherDimensionalAlgebraHDA), and how it can be completely specified for a Hausdorff space, X. Thus, in ref. [BHKP] Brown et al. associated to X a double groupoid, 𝝆2(X) , called the homotopy double groupoid of X which is completely defined by the data specified in Definitions 0.1 to 0.3 in this entry and related objects.

Generally, the geometry of squares and their compositionsMathworldPlanetmath leads to a common representation of a double groupoid in the following form:

𝖣= (0.1)