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weak homotopy double groupoid
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(Definition)
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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:
- 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.
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"weak homotopy double groupoid" is owned by bci1.
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(view preamble)
| Also defines: |
weak homotopy, weak homotopy equivalence relation, double groupoid |
| Keywords: |
weak homotopy, double groupoid |
Cross-references: groupoid, equivalence relation, homotopy, homotopy double groupoid of a Hausdorff space
There are 11 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 410 times total.
Classification:
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Pending Errata and Addenda
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