A model structure for the homotopy theory of crossed complexes

Ronald Brown; Marek Golasinski

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1989)

  • Volume: 30, Issue: 1, page 61-82
  • ISSN: 1245-530X

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Brown, Ronald, and Golasinski, Marek. "A model structure for the homotopy theory of crossed complexes." Cahiers de Topologie et Géométrie Différentielle Catégoriques 30.1 (1989): 61-82. <http://eudml.org/doc/91432>.

@article{Brown1989,
author = {Brown, Ronald, Golasinski, Marek},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {closed model category; Crossed complexes; crossed module structure; Quillen model category structure; weak equivalence; fibration; cofibration},
language = {eng},
number = {1},
pages = {61-82},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {A model structure for the homotopy theory of crossed complexes},
url = {http://eudml.org/doc/91432},
volume = {30},
year = {1989},
}

TY - JOUR
AU - Brown, Ronald
AU - Golasinski, Marek
TI - A model structure for the homotopy theory of crossed complexes
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1989
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 30
IS - 1
SP - 61
EP - 82
LA - eng
KW - closed model category; Crossed complexes; crossed module structure; Quillen model category structure; weak equivalence; fibration; cofibration
UR - http://eudml.org/doc/91432
ER -

References

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  5. 5 R. Brown, "Non-Abelian cohomology and the homotopy classification of maps", Homotopie algébrique et algèbre locale, Conf. Marseille-Luminy1982, ed. J.-M.Lemaire et J.-C. Thomas, Astérisque113-114 (1984), 167-172. Zbl0548.55018MR749052
  6. 6 R. Brown, "Coproducts of crossed P-modules: applications to second homotopy groups and to the homology of groups", Topology, 23 (1984), 337-345. Zbl0519.55009MR770569
  7. 7 R. Brown& P.J. Higgins, "The algebra of cubes", J. Pure Appl. Algebra21 (1981), 233-260. Zbl0468.55007MR617135
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  9. 9 R. Brown & P.J. Higgins, "Crossed complexes and non-Abelian extensions", Int. Conf. on Category Theory, Gummersbach (1981), Lecture Notes in Math.962, Springer (1982), 39-50. Zbl0504.55018MR682942
  10. 10 R. Brown& P.J. Higgins, "Tensor products and homotopies for ω-groupoids and crossed complexes ", J. Pure Appl. Algebra47 (1987), 1-33. Zbl0621.55009
  11. 11 R. Brown & P.J. Higgins, "The classifying space of a crossed complex" (in preparation). Zbl0732.55007
  12. 12 R. Brown & P.J. Higgins, "The relation between crossed complexes and chain complexes with a groupoid of operators" (in preparation). Zbl0691.18003
  13. 13 R. Brown & J. Huebschmann, "Identitites among relations", in Low-dimensional Topology, ed. R. Brown & T.L. Thickstun, London Math. Soc. Lecture Notes Series 48, C.U. P. (1982), 153-202. Zbl0485.57001MR662431
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  18. 18 K.H. Kamps, "Kan-Bedingungen und abstrakte Homotopietheorie ", Math. Z.124 (1972), 215-236. Zbl0223.55020MR295346
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  28. 28 R. Brown & P.J. Higgins, "Non-abelian cohomology with coefficients in a crossed complex" (in preparation). 

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