Homotopy theory for (braided) cat-groups
Garzon, Antonio R. ; Miranda, Jesus G.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997), p. 99-139 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CTGDC_1997__38_2_99_0,
     author = {Garzon, Antonio R. and Miranda, Jesus G.},
     title = {Homotopy theory for (braided) cat-groups},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {38},
     year = {1997},
     pages = {99-139},
     mrnumber = {1454159},
     zbl = {0880.18006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1997__38_2_99_0}
}

Garzon, Antonio R.; Miranda, Jesus G. Homotopy theory for (braided) cat-groups. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) pp. 99-139. http://gdmltest.u-ga.fr/item/CTGDC_1997__38_2_99_0/

[1] M.G. Barratt, Track groups II, Proc. London Math. Soc. (3) 5 (1955), 258-329. | MR 73179 | Zbl 0065.16302

[2] H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, de Gruyter Expos. Math. vol. 2, 1991. | MR 1096295 | Zbl 0716.55001

[3] A.L. Blakers, On the relations between homotopy and homology groups, Ann. of Math. vol. 49 (1948), 428-461. | MR 24132 | Zbl 0040.25701

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

[5] R. Brown and N.D. Gilbert, Algebraic models of 3-types and automorphism structures for crossed modules, Proc. London Math. Soc. (3) 59 (1989), 51-73. | MR 997251 | Zbl 0645.18007

[6] R. Brown and M. Golasinski, A model structure for the homotopy category of crossed complexes, Cahiers Topologie Géom. Diff. Catégoriques 30 (1989), 61-82. | Numdam | MR 1000831 | Zbl 0679.55016

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

[8] R. Brown and P.J. Higgins, The algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260. | MR 617135 | Zbl 0468.55007

[9] R. Brown and P.J. Higgins, Crossed complexes and chain complexes with operators, Math Proc. Camb. Phil. Soc. 107 (1990), 33-57. | MR 1021872 | Zbl 0691.18003

[10] R. Brown and P.J. Higgins, The classifying space of a crossed complex, Math Proc. Camb. Phil. Soc. 110 (1991), 95-120. | MR 1104605 | Zbl 0732.55007

[11] R. Brown and J.L. Loday, Van Kampen theorems for diagram of spaces, Topology 26 (1987), 311-335. | MR 899052 | Zbl 0622.55009

[12] M. Bullejos and A.M. Cegarra, A 3-dimensional nonabelian cohomology with applications to homotopy classification of continuous maps, Canadian Journal of Mathematics, 43 (2) (1991), 265-296. | MR 1113754 | Zbl 0726.18009

[13] M. Bullejos, P. Carrasco and A.M. Cegarra, Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg-MacLane's classification theorem, Math. Proc. Camb. Phil. Soc. 114 (1993), 163-189. | MR 1219923 | Zbl 0787.55007

[14] J.G. Cabello and A.R. Garzon, Closed model structures for algebraic models of n-types, J. Pure Appl. Algebra 103 (1995), 287-302. | MR 1357790 | Zbl 0837.55014

[15] P. Carrasco and A.M. Cegarra, Group theoretic algebraic models for homotopy types, J. Pure Appl. Algebra 75 (1991), 195-235. | MR 1137837 | Zbl 0742.55003

[16] P. Carrasco and A.M. Cegarra, Applications de la notion du Nerf d'une Gr-catégorie (tressée), C. R. Acad. Sci. Paris t. 321, Série I (1995), 395-398. | MR 1351084 | Zbl 0856.18005

[17] P. Carrasco and A.M. Cegarra, Extensions centrales de Gr-catégories par des Gr-catégories tressées, C. R. Acad. Sci. Paris t. 321, Série I (1995), 527-530. | MR 1356547 | Zbl 0856.18006

[18] D. Conduche, Modules croisés généralisés de longeur 2, J. Pure Appl. Algebra 34 (1984), 155-178. | MR 772056 | Zbl 0554.20014

[19] G. Ellis, Crossed squares and combinatorial homotopy, Math. Z. 214 (1993), 93-110. | MR 1234600 | Zbl 0789.55008

[20] A.R. Garzon and J.G. Miranda, Models for homotopy n-types in diagram categories, Applied Categorical Structures 4, (1996), 1-14. | MR 1406099 | Zbl 0858.55009

[21] D. Guin-Walery and J.L. Loday, Obstructions a l'excision en K-theorie algébrique, L. N. in Math 854 Springer (1981), 179-216. | MR 618305 | Zbl 0461.18007

[22] J. Howie, Pullback functors and crossed complexes, Cah. Top. Géom. Diff. XX-3 (1979), 281-296. | Numdam | MR 557084 | Zbl 0429.18007

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

[24] A. Joyal and R. Street, Braided tensor categories, Advances in Math. (1) 82 (1991), 20-78. | MR 1250465 | Zbl 0817.18007

[25] J.L. Loday, Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202. | MR 651845 | Zbl 0491.55004

[26] S. M and J.H.C. Whitehead, On the 3-type of a complex, Proc. Nat. Acac. Sci. USA 30 (1956), 41-48. | MR 33519 | Zbl 0035.39001

[27] J.G. Miranda, Estructuras de modelos y teoría de homotopía en categorías de grupos y grupoides simpliciales, Ph.D. thesis, University of Granada (1995).

[28] I. Moerdijk and J. Svensson, Algebraic classification of equi-variant homotopy 2-types, I, J. Pure Appl. Algebra 89, (1993), 187-216. | MR 1239560 | Zbl 0787.55008

[29] T. Porter, Abstract Homotopy theory. The interaction of category theory and homotopy theory, U. C. N. W. Maths Preprint 92.04 (1992). | MR 1957710

[30] D. Quillen, Homotopical Algebra, L.N. in Math. 43, Springer (1967). | MR 223432 | Zbl 0168.20903

[31] D. Quillen, Rational homotopy theory, Annals of Math. 90 (1969), 205-295. | MR 258031 | Zbl 0191.53702

[32] J.H.C. Whitehead, Combinatorial homotopy II, Bull. A.M.S. 55 (1949), 453-496. | MR 30760 | Zbl 0040.38801

[33] J.H.C. Whitehead, Algebraic Homotopy Theory, Proc. Int. Congress of Mathematicians, Harvard 2 (1950), 354-357. | MR 45389 | Zbl 0049.24103