@article{CTGDC_1989__30_1_61_0, author = {Brown, Ronald and Golasi\'nski, Marek}, title = {A model structure for the homotopy theory of crossed complexes}, journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, volume = {30}, year = {1989}, pages = {61-82}, mrnumber = {1000831}, zbl = {0679.55016}, language = {en}, url = {http://dml.mathdoc.fr/item/CTGDC_1989__30_1_61_0} }
Brown, Ronald; Golasinski, Marek. A model structure for the homotopy theory of crossed complexes. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 30 (1989) pp. 61-82. http://gdmltest.u-ga.fr/item/CTGDC_1989__30_1_61_0/
1 Algebraic homotopy, Cambridge University Press, Cambridge, 1989. | MR 985099 | Zbl 0688.55001
,2 The homotopy types of 4-dimensionsal complexes", Preprint, Bonn 1986. | MR 1361886
, "3 Fibrations of groupoids", J. Algebra 15 (1970), 103-132. | MR 271194 | Zbl 0194.02202
, "4 "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 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 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 The algebra of cubes", J. Pure Appl. Algebra 21 (1981), 233-260. | MR 617135 | Zbl 0468.55007
& , "8 Colimit theorems for relative homotopy groups", J. Pure Appl. Algebra 22 (1981), 11-41. | MR 621285 | Zbl 0475.55009
& , "9 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 Tensor products and homotopies for ω-groupoids and crossed complexes ", J. Pure Appl. Algebra 47 (1987), 1-33. | Zbl 0621.55009
& , "11 The classifying space of a crossed complex" (in preparation). | Zbl 0732.55007
& , "12 The relation between crossed complexes and chain complexes with a groupoid of operators" (in preparation).
& , "13 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 Calculus of fractions and homotopy theory, Springer-Verlag, Berlin 1967. | MR 210125 | Zbl 0186.56802
& ,15 An interpretation of the cohomology groups Hn(G,M) ", J. Alg. 16 (1970), 307-318. | Zbl 0699.20040
, "16 Pullback functors and crossed complexes", Cahiers de Top. et Géom. Diff. XX (1979), 281-295. | Numdam | MR 557084 | Zbl 0429.18007
, "17 Crossed n-fold extensions and cohomology", Comm. Math. Helv. 55 (1980), 302-314. | MR 576608 | Zbl 0443.18019
, "18 Kan-Bedingungen und abstrakte Homotopietheorie ", Math. Z. 124 (1972), 215-236. | MR 295346 | Zbl 0223.55020
, "19 Abstract homotopy and simple homotopy theory", U.C.N.W. Pure Maths, Preprint 86.9. | MR 1464944
& , "20 Cohomology of groups relative to a variety ", J. Alg. 69, (1979), 319-320. | MR 613866 | Zbl 0468.20044
, "21 Historical note", J. Alg. 69 (1979), 319-320.
, "22 Homotopical algebra", Lecture Notes in Math. 43, Springer (1967). | MR 223432 | Zbl 0168.20903
, "23 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 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 A note on homotopy equivalences", Proc. A.M.S. 32 (1972), 627-62. | MR 293632 | Zbl 0241.55009
, "26 Combinatorial homotopy II", Bull. A. M.S. 55 (1949), 453-469. | MR 30760 | Zbl 0040.38801
, "27 Simple homotopy type", Amer. J. Math. 72 (1950), 1-57. | MR 35437 | Zbl 0040.38901
, "28 Non-abelian cohomology with coefficients in a crossed complex" (in preparation).
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