@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},
year = {1997},
publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
volume = {38},
number = {2},
mrnumber = {1454159},
zbl = {0880.18006},
language = {en},
url = {https://www.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 - https://www.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 https://www.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. https://www.numdam.org/item/CTGDC_1997__38_2_99_0/
[1] , Track groups II, Proc. London Math. Soc. (3) 5 (1955), 258-329. | Zbl | MR
[2] , Combinatorial homotopy and 4-dimensional complexes, de Gruyter Expos. Math. vol. 2, 1991. | Zbl | MR
[3] , On the relations between homotopy and homology groups, Ann. of Math. vol. 49 (1948), 428-461. | Zbl | MR
[4] , Fibrations of groupoids, J. of Algebra 15 (1970), 103-132. | Zbl | MR
[5] and , Algebraic models of 3-types and automorphism structures for crossed modules, Proc. London Math. Soc. (3) 59 (1989), 51-73. | Zbl | MR
[6] and , A model structure for the homotopy category of crossed complexes, Cahiers Topologie Géom. Diff. Catégoriques 30 (1989), 61-82. | Zbl | MR | Numdam
[7] and , Tensor products and homotopies for ω-groupoids and crossed complexes, J. Pure Appl. Algebra 47 (1987), 1-33. | Zbl
[8] and , The algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260. | Zbl | MR
[9] and , Crossed complexes and chain complexes with operators, Math Proc. Camb. Phil. Soc. 107 (1990), 33-57. | Zbl | MR
[10] and , The classifying space of a crossed complex, Math Proc. Camb. Phil. Soc. 110 (1991), 95-120. | Zbl | MR
[11] and , Van Kampen theorems for diagram of spaces, Topology 26 (1987), 311-335. | Zbl | MR
[12] and , A 3-dimensional nonabelian cohomology with applications to homotopy classification of continuous maps, Canadian Journal of Mathematics, 43 (2) (1991), 265-296. | Zbl | MR
[13] , and , Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg-MacLane's classification theorem, Math. Proc. Camb. Phil. Soc. 114 (1993), 163-189. | Zbl | MR
[14] and , Closed model structures for algebraic models of n-types, J. Pure Appl. Algebra 103 (1995), 287-302. | Zbl | MR
[15] and , Group theoretic algebraic models for homotopy types, J. Pure Appl. Algebra 75 (1991), 195-235. | Zbl | MR
[16] and , Applications de la notion du Nerf d'une Gr-catégorie (tressée), C. R. Acad. Sci. Paris t. 321, Série I (1995), 395-398. | Zbl | MR
[17] and , Extensions centrales de Gr-catégories par des Gr-catégories tressées, C. R. Acad. Sci. Paris t. 321, Série I (1995), 527-530. | Zbl | MR
[18] , Modules croisés généralisés de longeur 2, J. Pure Appl. Algebra 34 (1984), 155-178. | Zbl | MR
[19] , Crossed squares and combinatorial homotopy, Math. Z. 214 (1993), 93-110. | Zbl | MR
[20] and , Models for homotopy n-types in diagram categories, Applied Categorical Structures 4, (1996), 1-14. | Zbl | MR
[21] and , Obstructions a l'excision en K-theorie algébrique, L. N. in Math 854 Springer (1981), 179-216. | Zbl | MR
[22] , Pullback functors and crossed complexes, Cah. Top. Géom. Diff. XX-3 (1979), 281-296. | Zbl | MR | Numdam
[23] , Crossed n-fold extensions and cohomology, Comm. Math. Helv. 55 (1980), 302-314. | Zbl | MR
[24] and , Braided tensor categories, Advances in Math. (1) 82 (1991), 20-78. | Zbl | MR
[25] , Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202. | Zbl | MR
[26] and , On the 3-type of a complex, Proc. Nat. Acac. Sci. USA 30 (1956), 41-48. | Zbl | MR
[27] , Estructuras de modelos y teoría de homotopía en categorías de grupos y grupoides simpliciales, Ph.D. thesis, University of Granada (1995).
[28] and , Algebraic classification of equi-variant homotopy 2-types, I, J. Pure Appl. Algebra 89, (1993), 187-216. | Zbl | MR
[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). | Zbl | MR
[31] , Rational homotopy theory, Annals of Math. 90 (1969), 205-295. | Zbl | MR
[32] , Combinatorial homotopy II, Bull. A.M.S. 55 (1949), 453-496. | Zbl | MR
[33] , Algebraic Homotopy Theory, Proc. Int. Congress of Mathematicians, Harvard 2 (1950), 354-357. | Zbl | MR





