Théorie de Schreier supérieure
Breen, Lawrence
Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992), p. 465-514 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1992_4_25_5_465_0,
     author = {Breen, Lawrence},
     title = {Th\'eorie de Schreier sup\'erieure},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {25},
     year = {1992},
     pages = {465-514},
     doi = {10.24033/asens.1656},
     mrnumber = {93k:18019},
     zbl = {0795.18009},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1992_4_25_5_465_0}
}

Breen, Lawrence. Théorie de Schreier supérieure. Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992) pp. 465-514. doi : 10.24033/asens.1656. http://gdmltest.u-ga.fr/item/ASENS_1992_4_25_5_465_0/

[1] J. Benabou, Catégories avec multiplication (C. R. Acad. Sc. Paris, vol. 256, 1963, p. 1887-1890). | MR 26 #6225 | Zbl 0111.02201

[2] A. J. Berrick, Group Extensions and their Trivialisations (L'Enseignement Math., vol. 31, 1985, p. 151-172). | MR 87d:20042 | Zbl 0584.20023

[3] P. Booth, P. Heath, C. Morgan et R. Piccinini, H-Spaces of Self-Equivalences of Fibrations and Bundles (Proc. London, Math. Soc., vol. 49, 1984, p. 111-127). | MR 85k:55013 | Zbl 0525.55005

[4] L. Breen, Bitorseurs et cohomologie non-abélienne, dans The Grothendieck Festchrift I (Progress in Mathematics, vol. 86, 1990, p. 401-476, Birkhäuser). | MR 92m:18019 | Zbl 0743.14034

[5] K. S. Brown, Cohomology of Groups (Graduate Texts in Mathematics, vol. 87, Springer-Verlag, 1982). | MR 83k:20002 | Zbl 0584.20036

[6] R. Brown et N. D. Gilbert, Algebraic Models of 3-Types and Automorphism Structures for Crossed Modules (Proc. London Math. Soc., vol. 59, 1989, p. 51-73). | MR 90e:18015 | Zbl 0645.18007

[7] M. Bullejos et A. Cegarra, A 3-Dimensional Non-Abelian Cohomology of Groups with Applications to Homotopy Classification of Continuous Maps (Canad. J. Math., vol. 43, (2), 1991, p. 1-32). | MR 92k:18012 | Zbl 0726.18009

[8] D. Conduché, Modules croisés généralisés de longueur 2 (J. Pure Applied Alg., vol. 34, 1984, p. 155-178). | MR 86g:20068 | Zbl 0554.20014

[9] P. Dedecker, Les foncteurs Extπ, H²π et H²π non abélien (C. R. Acad. Sci. Paris., vol. 258, 1964, p. 4891-4894). | MR 29 #5873 | Zbl 0124.01402

[10] P. Dedecker, Algèbre homologique non-abélienne (Colloque de Topologie Algébrique, Centre Belge de Recherches Mathématiques, Bruxelles, 1964). | Zbl 0168.26805

[11] P. Dedecker, Three Dimensional Non Abelian Cohomology Groups, dans Category Theory, Homology Theory and their Applications II (Lecture Notes in Math., vol. 92, 1969, p. 32-64, Springer-Verlag). | MR 41 #8493 | Zbl 0249.18027

[12] P. Deligne, La formule de dualité globale, exposé XVIII de SGA 4 (Lecture Notes in Math., vol. 305, Springer-Verlag, 1973). | MR 50 #7132 | Zbl 0259.14006

[13] M. Dror et A. Zabrodsky, Unipotency and Nilpotency in Homotopy Equivalences (Topology, vol. 18, 1979, p. 187-197). | MR 81g:55008 | Zbl 0417.55008

[14] J. Duskin, An Outline of a Theory of Higher Dimensional Descent (Bull. de la Soc. Math. de Belgique (série A), vol. 41, 1989, p. 249-277). | MR 91c:18013 | Zbl 0781.18004

[15] S. Eilenberg et S. Maclane, Cohomology theory in abstract groups I (Ann. of Math., vol. 47, 1948, p. 51-78). | MR 8,367f | Zbl 0029.34001

[16] S. Eilenberg et S. Maclane, On the Groups H(П, n) I, II (Ann. of Math., vol. 58, 1953, p. 55-106 et vol. 60, 1954, p. 49-139). | MR 15,54b | Zbl 0055.41704

[17] G. Ellis et R. Steiner, Higher Dimensional Crossed Modules and the Homotopy Groups of (n + 1)-ads (J. Pure Appl. Algebra, vol. 46, 1987, p. 117-136). | MR 88j:55010 | Zbl 0622.55010

[18] J. Giraud, Cohomologie non abélienne (Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, vol. 179, Springer-Verlag, 1971). | MR 49 #8992 | Zbl 0226.14011

[19] A. Grothendieck, Biextensions de faisceaux de groupes, exposé VII de SGA7I, Groupes de monodromie en géométrie algébrique (Lecture notes in Math., vol. 288, Springer-Verlag, 1972). | MR 50 #7134 | Zbl 0247.14011

[20] M. Hakim, Topos annelé et schémas relatifs (Ergebnisse der Math. und ihrer Grenzgebiete, vol. 64, Springer Verlag, 1972). | MR 51 #500 | Zbl 0246.14004

[21] R. O. Hill Jr., Moore-Postnikov Towers for Fibrations in which π1 (fiber) is Non-Abelian (Pacific J. Math., vol. 62, 1976, p. 141-148). | Zbl 0328.55013

[22] D. F. Holt, An Interpretation of the Cohomology Groups Hn(G, A) (J. Algebra, vol. 60, 1979, p. 307-320). | MR 80m:20040 | Zbl 0699.20040

[23] J. Huebschmann, Crossed n-fold Extensions of Groups and Cohomology (Comment. Math. Helvetici, vol. 55, 1980, p. 302-314). | MR 82e:20063 | Zbl 0443.18019

[24] L. Illusie, Complexe cotangent et déformations I, II (Lecture notes in Math., vol. 239, 283, Springer-Verlag, 1971, 1972). | MR 58 #10886a | Zbl 0224.13014

[25] A. Joyal et R. Street, Braided Monoidal Categories, Preprint.

[26] G. M. Kelley et M. Laplaza, Coherence for Compact Closed Categories (Lecture notes in Math., vol. 281, Springer-Verlag, 1972).

[27] A. Legrand, Homotopie des espaces de sections (Lecture notes in Math., vol. 941, Springer-Verlag, 1982). | MR 83m:55028 | Zbl 0535.55001

[28] J.-L. Loday, Spaces with Finitely Many Non Trivial Homotopy Groups (J. Pure and Appl. Alg., vol. 24, 1982, p. 179-202). | MR 83i:55009 | Zbl 0491.55004

[29] S. Maclane, Natural Associativity and Commutativity (Rice University Studies, vol. 49, 1963, p. 28-46), reproduit dans les Selected Papers, I. KAPLANSKY éd., Springer Verlag, 1979. | MR 30 #1160 | Zbl 0244.18008

[30] S. Maclane, Categories for the Working Mathematician (Graduate texts in Mathematics, vol. 5, Springer-Verlag, 1972).

[31] J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, 1967. | MR 36 #5942 | Zbl 0165.26004

[32] J. P. May, E∞-Spaces, Group Completions and Permutative Categories, dans New Developments in Topology, G. SEGAL éd., (London Math. Soc. Lecture note series, vol. 11, 1974, p. 61-93, Cambridge University Press). | MR 49 #3915 | Zbl 0281.55003

[33] J. P. May, Classifying Spaces and Fibrations (Memoirs of the A.M.S., vol. 155, 1975). | MR 51 #6806 | Zbl 0321.55033

[34] I. Moerdijk, Morita Equivalence for Continuous Groups (Math. Proc. Cambr. Phil. Soc., vol. 103, 1988, p. 97-115). | MR 88j:22001 | Zbl 0648.22001

[35] G. Moore et N. Seiberg, Classical and Quantum Field Theory, (Comm. Math. Phys., vol. 123, 1989, p. 177-254). | MR 90e:81216 | Zbl 0694.53074

[36] K. Norrie, Actions and Automorphisms of Crossed Modules (Bull. S.M.F., vol. 118, 1989, p. 101-119). | Numdam | MR 91m:18010 | Zbl 0719.20018

[37] R. A. Piccinnini éd., Groups of Self-Equivalences and Related Topics (Lecture notes in Math., vol. 1425, Springer-Verlag, 1990). | MR 91e:55001 | Zbl 0695.00020

[38] N. Saavedra Rivano, Catégories tannakiennes (Lecture notes in Math., vol. 265, Springer-Verlag, 1972). | MR 49 #2769 | Zbl 0241.14008

[39] J. E. Roberts, Mathematical Aspects of Local Cohomology (Colloquium on Operator Algebras and their Applications to Mathematical Physics, Colloque International C.N.R.S., vol. 274, Marseille, 1977). | MR 81e:18017 | Zbl 0455.55005

[40] O. Schreier, Uber die Erweiterung von Gruppen I (Monatsh. Math. Phys., vol. 34, 1926, p. 165-180) ; II. (Abh. Math. Sem. Hamburg, vol. 4, 1926, p. 321-346). | JFM 52.0113.04

[41] G. Segal, Cohomology of Topological Groups (Symposia Mat. IV, 1970, p. 377-387, Istituto Nazionale di Alta Matematic, Bologna). | MR 43 #6292 | Zbl 0223.57034

[42] J.-P. Serre, Groupes algébriques et corps de classe (Actualités scientifiques et Industrielles, Hermann, 1959). | MR 21 #1973 | Zbl 0097.35604

[43] Hoang Xuan Sinh, Gr-catégories (thèse de doctorat, Université Paris-VII, 1975).

[44] J. Stasheff, Homotopy Associativity of H-Spaces I (Trans. A.M.S., vol. 108, 1963, p. 275-292). | MR 28 #1623 | Zbl 0114.39402

[45] J. Stasheff, H-Spaces from a Homotopy Point of View (Lecture Notes in Math., vol. 161, Springer-Verlag, 1970). | MR 42 #5261 | Zbl 0205.27701

[46] J. Stasheff, H-Spaces and Classifying Spaces : Foundations and Recent Developments, dans Algebraic Topology (Proc. Symp. Pure Math., vol. 22, 1971, p. 247-272, A.M.S.). | MR 47 #9612 | Zbl 0234.55020

[47] K. Ulbrich, Group Cohomology for Picard Categories (J. Alg., vol. 91, 1984, p. 464-498). | MR 86h:18003 | Zbl 0554.18005

[48] D. Yetter, Category Theoretic Representations of Knotted Graphs in S3 [Advances in Mathematics (à paraître)].