The equivalence of ω -groupoids and cubical T -complexes

Ronald Brown; Philip J. Higgins

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1981)

  • Volume: 22, Issue: 4, page 349-370
  • ISSN: 1245-530X

How to cite

top

Brown, Ronald, and Higgins, Philip J.. "The equivalence of $\omega $-groupoids and cubical $T$-complexes." Cahiers de Topologie et Géométrie Différentielle Catégoriques 22.4 (1981): 349-370. <http://eudml.org/doc/91279>.

@article{Brown1981,
author = {Brown, Ronald, Higgins, Philip J.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {cubical complexes; Kan complexes; T-complexes; thin elements; omega- groupoids; isomorphism of categories; Seifert-van Kampen theorem},
language = {eng},
number = {4},
pages = {349-370},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {The equivalence of $\omega $-groupoids and cubical $T$-complexes},
url = {http://eudml.org/doc/91279},
volume = {22},
year = {1981},
}

TY - JOUR
AU - Brown, Ronald
AU - Higgins, Philip J.
TI - The equivalence of $\omega $-groupoids and cubical $T$-complexes
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1981
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 22
IS - 4
SP - 349
EP - 370
LA - eng
KW - cubical complexes; Kan complexes; T-complexes; thin elements; omega- groupoids; isomorphism of categories; Seifert-van Kampen theorem
UR - http://eudml.org/doc/91279
ER -

References

top
  1. 1 N. Ashley, T-complexes and crossed complexes, Ph. D. Thesis, University of Wales, 1978. Zbl0558.55015MR766239
  2. 2 A.L. Blakers, Some relations between homology and homotopy groups, Ann. of Math.49 (1948), 428 - 461. Zbl0040.25701MR24132
  3. 3 R. Brown, Higher dimensional group theory, in Low dimensional topology, ed. Brown & Thickstun, London Math. Soc. Lecture Notes48, Cambridge, 1982. Zbl0484.55007MR662433
  4. 4 R. Brown& P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra, 21 (1981), 233- 260. Zbl0468.55007MR617135
  5. 5 R. Brown& P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra, 22 (1981), 11-41. Zbl0475.55009MR621285
  6. 6 R. Brown & P.J. Higgins, The equivalence of ∞-groupoids and crossed complexes, This same issue. 
  7. 7 M.K. Dakin, Kan complexes and multiple groupoid structures, Ph. D. Thesis, University of Wales, 1977. Zbl0566.55010MR766238
  8. 8 A. Dold, Homology of symmetric products and other functors of complexes, Ann. of Math.68 (1958), 54-80. Zbl0082.37701MR97057
  9. 9 J. Howie, Pullback functors and crossed complexes, Cahiers Topo. et Géom. Diff. XX-3 (1979), 281-296. Zbl0429.18007MR557084
  10. 10 D.M. Kan, Abstract homotopy theory I, Proc. Nat. Acad. Sci. U.S.A.41 (1955), 1092-1096. Zbl0065.38601MR79762
  11. 11 D.M. Kan, Functors involving c. s. s. complexes, Trans. A.M.S.87 (1958), 330 - 346. Zbl0090.39001MR131873
  12. 12 J.H.C. Whitehead, Combinatorial homotopy II, Bull. A.M.S.55 (1949), 453-496. Zbl0040.38801MR30760

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.