Théorie de Schreier supérieure

Breen, Lawrence

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 25 (1992) no. 5, pp. 465-514

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

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

[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). | Zbl | MR

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

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

[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). | Zbl | MR

[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). | Zbl | MR

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

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

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

[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). | Zbl | MR

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

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

[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). | Zbl | MR

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

[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). | Zbl | MR

[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). | Zbl | MR

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

[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). | Zbl | MR

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

[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

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

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

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

[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). | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

[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). | Zbl | MR

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

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

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

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

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

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

[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). | Zbl | MR

[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

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

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

[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). | Zbl | MR

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

[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.). | Zbl | MR

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

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