# homotopy double groupoid of a Hausdorff space

Homotopy double groupoid^{} of a Hausdorff space

Let $X$ be a Hausdorff space. Also consider the HDA concept of a
double groupoid^{} (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, ${\bm{\rho}}_{2}^{\mathrm{\square}}(X)$
, 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 compositions^{} leads to a common representation of a *double groupoid* in the following form:

$$\U0001d5a3=$$ | (0.1) |