Brown, Ronald; Golasinski, Marek
A model structure for the homotopy theory of crossed complexes
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 30 (1989) no. 1 , p. 61-82
Zbl 0679.55016 | MR 1000831 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=CTGDC_1989__30_1_61_0

Bibliographie

1 H.J. Baues, Algebraic homotopy, Cambridge University Press, Cambridge, 1989. MR 985099 | Zbl 0688.55001

2 H.J. Baues, "The homotopy types of 4-dimensionsal complexes", Preprint, Bonn 1986. MR 1361886

3 R. Brown, "Fibrations of groupoids", J. Algebra 15 (1970), 103-132. MR 271194 | Zbl 0194.02202

4 R. Brown, "Some non-abelian methods in homotopy theory and homological algebra", Categorical topology, Proc. Conf. on Categorical Topology, Toledo, Ohio 1983, ed. H.L. Bentley et al, Heldermann-Verlag, Berlin (1984), 108-146. MR 785014 | Zbl 0558.55001

5 R. Brown, "Non-Abelian cohomology and the homotopy classification of maps", Homotopie algébrique et algèbre locale, Conf. Marseille-Luminy 1982, ed. J.-M.Lemaire et J.-C. Thomas, Astérisque 113-114 (1984), 167-172. MR 749052 | Zbl 0548.55018

6 R. Brown, "Coproducts of crossed P-modules: applications to second homotopy groups and to the homology of groups", Topology, 23 (1984), 337-345. MR 770569 | Zbl 0519.55009

7 R. Brown& P.J. Higgins, "The algebra of cubes", J. Pure Appl. Algebra 21 (1981), 233-260. MR 617135 | Zbl 0468.55007

8 R. Brown& P.J. Higgins, "Colimit theorems for relative homotopy groups", J. Pure Appl. Algebra 22 (1981), 11-41. MR 621285 | Zbl 0475.55009

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. MR 682942 | Zbl 0504.55018

10 R. Brown& P.J. Higgins, "Tensor products and homotopies for ω-groupoids and crossed complexes ", J. Pure Appl. Algebra 47 (1987), 1-33. Zbl 0621.55009

11 R. Brown & P.J. Higgins, "The classifying space of a crossed complex" (in preparation). Zbl 0732.55007

12 R. Brown & P.J. Higgins, "The relation between crossed complexes and chain complexes with a groupoid of operators" (in preparation).

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. MR 662431 | Zbl 0485.57001

14 P. Gabriel& M. Zisman, Calculus of fractions and homotopy theory, Springer-Verlag, Berlin 1967. MR 210125 | Zbl 0186.56802

15 D.F. Holt, "An interpretation of the cohomology groups Hn(G,M) ", J. Alg. 16 (1970), 307-318. Zbl 0699.20040

16 J. Howie, "Pullback functors and crossed complexes", Cahiers de Top. et Géom. Diff. XX (1979), 281-295. Numdam | MR 557084 | Zbl 0429.18007

17 J. Huebschmann, "Crossed n-fold extensions and cohomology", Comm. Math. Helv. 55 (1980), 302-314. MR 576608 | Zbl 0443.18019

18 K.H. Kamps, "Kan-Bedingungen und abstrakte Homotopietheorie ", Math. Z. 124 (1972), 215-236. MR 295346 | Zbl 0223.55020

19 K.H. Kamps & T. Porter, "Abstract homotopy and simple homotopy theory", U.C.N.W. Pure Maths, Preprint 86.9. MR 1464944

20 A.S.-T. Lue, "Cohomology of groups relative to a variety ", J. Alg. 69, (1979), 319-320. MR 613866 | Zbl 0468.20044

21 S. Mac Lane, "Historical note", J. Alg. 69 (1979), 319-320.

22 D.G. Quillen, "Homotopical algebra", Lecture Notes in Math. 43, Springer (1967). MR 223432 | Zbl 0168.20903

23 C.B. Spencer, "An abstract setting for homotopy pushouts and pullbacks", Cahiers de Top. et Géom. Diff. XVIII (1977), 409-429. Numdam | MR 486054 | Zbl 0378.18008

24 C.B. Spencer & Y.L. Wong, "Pullback and pushout squares in a special double category with connection", Cahiers de Top. et Géom. Diff. XXIV (1983). 161-192. Numdam | MR 710039 | Zbl 0519.18008

25 R.M. Vogt, "A note on homotopy equivalences", Proc. A.M.S. 32 (1972), 627-62. MR 293632 | Zbl 0241.55009

26 J.H.C. Whitehead, "Combinatorial homotopy II", Bull. A. M.S. 55 (1949), 453-469. MR 30760 | Zbl 0040.38801

27 J.H.C. Whitehead, "Simple homotopy type", Amer. J. Math. 72 (1950), 1-57. MR 35437 | Zbl 0040.38901

28 R. Brown & P.J. Higgins, "Non-abelian cohomology with coefficients in a crossed complex" (in preparation).