weak homotopy double groupoid

Definition 0.1.

a weak homotopy double groupoidPlanetmathPlanetmath (WHDG) of a compactly–generated space Xcg, (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 relationMathworldPlanetmath from the cited ref. with the weak homotopy equivalence relationMathworldPlanetmathPlanetmathPlanetmath in the definition of the fundamental groupoidMathworldPlanetmathPlanetmathPlanetmath, as well as replacing the Hausdorff space by the compactly-generated space Xcg. Therefore, the weak homotopyMathworldPlanetmathPlanetmath data for the weak homotopy double groupoid of Xcg, 𝝆(Xcg), 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.
Title weak homotopy double groupoid
Canonical name WeakHomotopyDoubleGroupoid
Date of creation 2013-03-22 18:15:12
Last modified on 2013-03-22 18:15:12
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 16
Author bci1 (20947)
Entry type Definition
Classification msc 55N33
Classification msc 55N20
Classification msc 55P10
Classification msc 55U40
Classification msc 18B40
Classification msc 18D05
Synonym homotopy double groupoid
Related topic WeakHomotopyAdditionLemma
Related topic OmegaSpectrum
Related topic FEquivalenceInCategory
Defines higher dimensional weak homotopy