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weak homotopy double groupoid (Definition)
Definition 0.1   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. [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 $X_{cg}$. Therefore, the weak homotopy data for the weak homotopy double groupoid of $X_{cg}$, $\boldsymbol{\rho}^{\square} (X_{cg})$, will now be:

\begin{displaymath} \begin{array}{c} (\boldsymbol{\rho}^{\square}_2 (X), \boldsy... ...X , \partial^{-} , \partial^{+} , + , \varepsilon). \end{array}\end{displaymath}

Bibliography

1
R. Brown, K.A. Hardie, K.H. Kamps and T. Porter, A homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories 10,(2002): 71-93.



"weak homotopy double groupoid" is owned by bci1.

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Also defines:  weak homotopy, weak homotopy equivalence relation, double groupoid
Keywords:  weak homotopy, double groupoid

Cross-references: fundamental groupoid, equivalence relation, homotopy, regular
There are 17 references to this object.

This is version 2 of weak homotopy double groupoid, born on 2009-05-12, modified 2009-05-12.
Object id is 750, canonical name is WeakHomotopyDoubleGroupoid.
Accessed 1099 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
Pending Errata and Addenda
None.
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