@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}, pages = {99--139}, publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS}, volume = {38}, number = {2}, year = {1997}, mrnumber = {1454159}, zbl = {0880.18006}, language = {en}, url = {http://archive.numdam.org/item/CTGDC_1997__38_2_99_0/} }
TY - JOUR AU - Garzon, Antonio R. AU - Miranda, Jesus G. TI - Homotopy theory for (braided) cat-groups JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques PY - 1997 SP - 99 EP - 139 VL - 38 IS - 2 PB - Dunod éditeur, publié avec le concours du CNRS UR - http://archive.numdam.org/item/CTGDC_1997__38_2_99_0/ LA - en ID - CTGDC_1997__38_2_99_0 ER -
%0 Journal Article %A Garzon, Antonio R. %A Miranda, Jesus G. %T Homotopy theory for (braided) cat-groups %J Cahiers de Topologie et Géométrie Différentielle Catégoriques %D 1997 %P 99-139 %V 38 %N 2 %I Dunod éditeur, publié avec le concours du CNRS %U http://archive.numdam.org/item/CTGDC_1997__38_2_99_0/ %G en %F 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) no. 2, pp. 99-139. http://archive.numdam.org/item/CTGDC_1997__38_2_99_0/
[1] Track groups II, Proc. London Math. Soc. (3) 5 (1955), 258-329. | MR | Zbl
,[2] Combinatorial homotopy and 4-dimensional complexes, de Gruyter Expos. Math. vol. 2, 1991. | MR | Zbl
,[3] On the relations between homotopy and homology groups, Ann. of Math. vol. 49 (1948), 428-461. | MR | Zbl
,[4] Fibrations of groupoids, J. of Algebra 15 (1970), 103-132. | MR | Zbl
,[5] Algebraic models of 3-types and automorphism structures for crossed modules, Proc. London Math. Soc. (3) 59 (1989), 51-73. | MR | Zbl
and ,[6] A model structure for the homotopy category of crossed complexes, Cahiers Topologie Géom. Diff. Catégoriques 30 (1989), 61-82. | Numdam | MR | Zbl
and ,[7] Tensor products and homotopies for ω-groupoids and crossed complexes, J. Pure Appl. Algebra 47 (1987), 1-33. | Zbl
and ,[8] The algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260. | MR | Zbl
and ,[9] Crossed complexes and chain complexes with operators, Math Proc. Camb. Phil. Soc. 107 (1990), 33-57. | MR | Zbl
and ,[10] The classifying space of a crossed complex, Math Proc. Camb. Phil. Soc. 110 (1991), 95-120. | MR | Zbl
and ,[11] Van Kampen theorems for diagram of spaces, Topology 26 (1987), 311-335. | MR | Zbl
and ,[12] A 3-dimensional nonabelian cohomology with applications to homotopy classification of continuous maps, Canadian Journal of Mathematics, 43 (2) (1991), 265-296. | MR | Zbl
and ,[13] 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 | Zbl
, and ,[14] Closed model structures for algebraic models of n-types, J. Pure Appl. Algebra 103 (1995), 287-302. | MR | Zbl
and ,[15] Group theoretic algebraic models for homotopy types, J. Pure Appl. Algebra 75 (1991), 195-235. | MR | Zbl
and ,[16] Applications de la notion du Nerf d'une Gr-catégorie (tressée), C. R. Acad. Sci. Paris t. 321, Série I (1995), 395-398. | MR | Zbl
and ,[17] Extensions centrales de Gr-catégories par des Gr-catégories tressées, C. R. Acad. Sci. Paris t. 321, Série I (1995), 527-530. | MR | Zbl
and ,[18] Modules croisés généralisés de longeur 2, J. Pure Appl. Algebra 34 (1984), 155-178. | MR | Zbl
,[19] Crossed squares and combinatorial homotopy, Math. Z. 214 (1993), 93-110. | MR | Zbl
,[20] Models for homotopy n-types in diagram categories, Applied Categorical Structures 4, (1996), 1-14. | MR | Zbl
and ,[21] Obstructions a l'excision en K-theorie algébrique, L. N. in Math 854 Springer (1981), 179-216. | MR | Zbl
and ,[22] Pullback functors and crossed complexes, Cah. Top. Géom. Diff. XX-3 (1979), 281-296. | Numdam | MR | Zbl
,[23] Crossed n-fold extensions and cohomology, Comm. Math. Helv. 55 (1980), 302-314. | MR | Zbl
,[24] Braided tensor categories, Advances in Math. (1) 82 (1991), 20-78. | MR | Zbl
and ,[25] Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202. | MR | Zbl
,[26] On the 3-type of a complex, Proc. Nat. Acac. Sci. USA 30 (1956), 41-48. | MR | Zbl
and ,[27] Estructuras de modelos y teoría de homotopía en categorías de grupos y grupoides simpliciales, Ph.D. thesis, University of Granada (1995).
,[28] Algebraic classification of equi-variant homotopy 2-types, I, J. Pure Appl. Algebra 89, (1993), 187-216. | MR | Zbl
and ,[29] Abstract Homotopy theory. The interaction of category theory and homotopy theory, U. C. N. W. Maths Preprint 92.04 (1992). | MR
,[30] Homotopical Algebra, L.N. in Math. 43, Springer (1967). | MR | Zbl
,[31] Rational homotopy theory, Annals of Math. 90 (1969), 205-295. | MR | Zbl
,[32] Combinatorial homotopy II, Bull. A.M.S. 55 (1949), 453-496. | MR | Zbl
,[33] Algebraic Homotopy Theory, Proc. Int. Congress of Mathematicians, Harvard 2 (1950), 354-357. | MR | Zbl
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