The equivalence of ∞ -groupoids and crossed complexes

Ronald Brown; Philip J. Higgins

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1981)

  • Volume: 22, Issue: 4, page 371-386
  • ISSN: 1245-530X

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Brown, Ronald, and Higgins, Philip J.. "The equivalence of $\infty $-groupoids and crossed complexes." Cahiers de Topologie et Géométrie Différentielle Catégoriques 22.4 (1981): 371-386. <http://eudml.org/doc/91280>.

@article{Brown1981,
author = {Brown, Ronald, Higgins, Philip J.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {n-fold categories; equivalence of categories; infinity-groupoids; crossed complexes; omega-groupoids},
language = {eng},
number = {4},
pages = {371-386},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {The equivalence of $\infty $-groupoids and crossed complexes},
url = {http://eudml.org/doc/91280},
volume = {22},
year = {1981},
}

TY - JOUR
AU - Brown, Ronald
AU - Higgins, Philip J.
TI - The equivalence of $\infty $-groupoids and crossed 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 - 371
EP - 386
LA - eng
KW - n-fold categories; equivalence of categories; infinity-groupoids; crossed complexes; omega-groupoids
UR - http://eudml.org/doc/91280
ER -

References

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  1. 1 R. Brown& P.J. Higgins, On the algebra of cubes, J. Pure & Appl. Algebra, 21 (1981), 233- 260. Zbl0468.55007MR617135
  2. 2 R. Brown& P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure & Appl. Algebra22 (1981), 11-41. Zbl0475.55009MR621285
  3. 3 R. Brown & P.J. Higgins, The equivalence of ω-groupoids and cubical T-complexe s, This issue. 
  4. 4 R. Brown & C.B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Kon. Akad. v. Wet.79 (1976), 296. Zbl0333.55011MR419643
  5. 5 R. Brown & C.B. Spencer, Double groupoids and crossed modules,Cahiers Top. et Géom. Diff.XVII-4 (1976), 343-362. Zbl0344.18004MR440553
  6. 6 M.K. Dakin, Kan complexes and multiple groupoid structures, Ph. D. Thesis University of Wale s, 1977. Zbl0566.55010MR766238
  7. 7 A. Dold, Homology of symmetric products and other functors of complexes, Ann. of Math.68 (1958), 54 - 80. Zbl0082.37701MR97057
  8. 8 A. & C. Ehresmann, Multiple functors II, III, Cahiers Top. et Géom. Diff.xx (1978), 295-333, 387-443. Zbl0415.18006
  9. 9 D.M. Kan, Functors involving c.s.s. complexes, Trans. A.M.S.87 (1958), 330. Zbl0090.39001MR131873
  10. 10 C.B. Sp Encer, An abstract setting for homotopy pushouts and pullbacks, Cahiers Top. et Géom. Diff. XVIII-4 (1977), 409-430. Zbl0378.18008MR486054
  11. 11 O. Wyler, Multiple functor categories, Mimeographed Note s, Camegie-Mellon University, 1972. 

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