Definition 0.1
a weak homotopy double groupoid (WHDG) of a
compactly-generated space 
, (weak Hausdorff space) is
defined through a construction method similar to that developed by R. Brown (ref. [
1]) for the
homotopy double groupoid of a Hausdorff space. The key changes here involve replacing the
regular
homotopy
equivalence relation
from the cited ref. with the
weak homotopy equivalence relation in the definition of the
fundamental groupoid, as well as replacing the Hausdorff space by the compactly-generated space

. Therefore, the weak homotopy data for the
weak homotopy double groupoid of

,

, will now be: