PlanetPhysics/Weak Homotopy Double Groupoid

a weak homotopy double groupoid (WHDG) of a compactly--generated space $X_{cg}$, (weak Hausdorff space) is defined through a construction method similar to that developed by R. Brown (ref. ) for the homotopy double groupoid of a Hausdorff space . The key changes here involve replacing the [[../CoIntersections/|regular]] [[../ThinEquivalence/|homotopy]] [[../TrivialGroupoid/|equivalence relation]] from the cited ref. with the weak homotopy equivalence relation in the definition of the [[../CubicalHigherHomotopyGroupoid/|fundamental groupoid]], as well as replacing the Hausdorff space by the compactly-generated space $X_{cg}$. Therefore, the weak homotopy data for the weak homotopy double groupoid of $X_{cg}$, ${\mathit{\rho }}^{◻}(X_{cg})$, will now be: \\

Failed to parse (unknown function "\begin{matrix}"): {\displaystyle \begin{matrix} (\boldsymbol{\rho}^{\square}_2 (X), \boldsymbol{\rho}_1^{\square} (X) , \partial^{-}_{1} , \partial^{+}_{1} , +_{1} , \varepsilon _{1}) , \boldsymbol{\rho}^{\square}_2 (X), \boldsymbol{\rho}^{\square}_1 (X) , \partial^{-}_{2} , \partial^{+}_{2} , +_{2} , \varepsilon _{2})\<blockquote><math>3mm] (\boldsymbol{\rho}^{\square}_1 (X) , X , \partial^{-} , \partial^{+} , + , \varepsilon). \end{matrix}}