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Brown, Ronald; Golasinski, Marek
A model structure for the homotopy theory of crossed complexes. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 30 no. 1 (1989), p. 61-82
Full text djvu | pdf | Reviews MR 1000831 | Zbl 0679.55016 | 2 citations in Numdam
stable URL: http://www.numdam.org/item?id=CTGDC_1989__30_1_61_0
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.
Article | 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). |
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