Geodesic
A homotopy double groupoid of a Hausdorff space
Theory and applications of categories, Tome 10 (2002), pp. 71-93.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We associate to a Hausdorff space, $ X $, a double groupoid, $ \mbox{\boldmath $ \rho $}^{\square}_{2} (X) $, the homotopy double groupoid of $ X $. The construction is based on the geometric notion of thin square. Under the equivalence of categories between small $ 2 $-categories and double categories with connection the homotopy double groupoid corresponds to the homotopy 2- groupoid, $ {\bf G}_{2} (X) $. The cubical nature of $ \mbox{\boldmath $ \rho $}^{\square}_{2} (X) $ as opposed to the globular nature of $ {\bf G}_{2} (X) $ should provide a convenient tool when handling `local-to-global' problems as encountered in a generalised van Kampen theorem and dealing with tensor products and enrichments of the category of compactly generated Hausdorff spaces.
Classification : 18D05, 20L05, 55Q05, 55Q35.
Keywords: double groupoid, connection, thin structure, 2-groupoid, double track, 2- track, thin square, homotopy addition lemma. 
@article{TAC_2002_10_a1,
     author = {Ronald Brown and Keith A. Hardie and Klaus Heiner Kamps and Timothy Porter},
     title = {A homotopy double groupoid of a {Hausdorff} space},
     journal = {Theory and applications of categories},
     pages = {71--93},
     publisher = {mathdoc},
     volume = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a1/}
}
TY  - JOUR
AU  - Ronald Brown
AU  - Keith A. Hardie
AU  - Klaus Heiner Kamps
AU  - Timothy Porter
TI  - A homotopy double groupoid of a Hausdorff space
JO  - Theory and applications of categories
PY  - 2002
SP  - 71
EP  - 93
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2002_10_a1/
LA  - en
ID  - TAC_2002_10_a1
ER  - 
%0 Journal Article
%A Ronald Brown
%A Keith A. Hardie
%A Klaus Heiner Kamps
%A Timothy Porter
%T A homotopy double groupoid of a Hausdorff space
%J Theory and applications of categories
%D 2002
%P 71-93
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2002_10_a1/
%G en
%F TAC_2002_10_a1
Ronald Brown; Keith A. Hardie; Klaus Heiner Kamps; Timothy Porter. A homotopy double groupoid of a Hausdorff space. Theory and applications of categories, Tome 10 (2002), pp. 71-93. http://geodesic.mathdoc.fr/item/TAC_2002_10_a1/