Algebraic & Geometric Topology Volume 12, issue 1 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Higher cohomologies of modules

María Calvo, Antonio M Cegarra and Nguyen T Quang

Algebraic & Geometric Topology 12 (2012) 343–413

DOI: 10.2140/agt.2012.12.343

Bibliography

1	E Aldrovandi, B Noohi, Butterflies I ; Morphisms of 2–group stacks, Adv. Math. 221 (2009) 687 MR2511036
2	J C Baez, A D Lauda, Higher-dimensional algebra V : 2–groups, Theory Appl. Categ. 12 (2004) 423 MR2068521
3	H J Baues, G Wirsching, Cohomology of small categories, J. Pure Appl. Algebra 38 (1985) 187 MR814176
4	F Borceux, Handbook of categorical algebra 1 : Basic category theory, 50, Cambridge Univ. Press (1994) MR1291599
5	D Bourn, E M Vitale, Extensions of symmetric cat-groups, Homology Homotopy Appl. 4 (2002) 103 MR1983014
6	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
7	L Breen, Théorie de Schreier supérieure, Ann. Sci. École Norm. Sup. 25 (1992) 465 MR1191733
8	L Breen, Monoidal categories and multiextensions, Compositio Math. 117 (1999) 295 MR1702420
9	R Brown, N D Gilbert, Algebraic models of 3–types and automorphism structures for crossed modules, Proc. London Math. Soc. 59 (1989) 51 MR997251
10	P Carrasco, A M Cegarra, Schreier theory for central extensions of categorical groups, Comm. Algebra 24 (1996) 4059 MR1414570
11	P Carrasco, A M Cegarra, A R Garzón, Nerves and classifying spaces for bicategories, Algebr. Geom. Topol. 10 (2010) 219 MR2602835
12	P Carrasco, A M Cegarra, A R Garzón, Classifying spaces for braided monoidal categories and lax diagrams of bicategories, Adv. Math. 226 (2011) 419 MR2735766
13	A M Cegarra, J M García-Calcines, J A Ortega, On graded categorical groups and equivariant group extensions, Canad. J. Math. 54 (2002) 970 MR1924710
14	A M Cegarra, A R Garzón, Homotopy classification of categorical torsors, Appl. Categ. Structures 9 (2001) 465 MR1865612
15	A M Cegarra, E Khmaladze, Homotopy classification of braided graded categorical groups, J. Pure Appl. Algebra 209 (2007) 411 MR2293318
16	A M Cegarra, E Khmaladze, Homotopy classification of graded Picard categories, Adv. Math. 213 (2007) 644 MR2332605
17	W Chachólski, J Scherer, Homotopy theory of diagrams, 155, no. 736, Amer. Math. Soc. (2002) MR1879153
18	D C Cisinski, F Déglise, Triangulated categories of mixed motives arXiv:0912.2110
19	D Conduché, Modules croisés généralisés de longueur 2, from: "Proceedings of the Luminy conference on algebraic K–theory (Luminy, 1983)" (editors E M Friedlander, M Karoubi) (1984) 155 MR772056
20	A H Copeland Jr., On H–spaces with two non-trivial homotopy groups, Proc. Amer. Math. Soc. 8 (1957) 184 MR0083737
21	P Deligne, La formule de dualité globale, from: "Théorie des topos et cohomologie étale des schémas. Tome 3. Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4), Vol. 3, Exp. No. XVIII", Lecture Notes in Math. 305, Springer (1973) 481 MR0354654
22	A Dold, D Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier Grenoble 11 (1961) 201 MR0150183
23	E Dror, W G Dwyer, D M Kan, Equivariant maps which are self homotopy equivalences, Proc. Amer. Math. Soc. 80 (1980) 670 MR587952
24	E Dror Farjoun, Homotopy and homology of diagrams of spaces, from: "Algebraic topology (Seattle, WA, 1985)" (editors H R Miller, D C Ravenel), Lecture Notes in Math. 1286, Springer (1987) 93 MR922924
25	E Dror Farjoun, A Zabrodsky, Homotopy equivalence between diagrams of spaces, J. Pure Appl. Algebra 41 (1986) 169 MR849903
26	W G Dwyer, D M Kan, An obstruction theory for diagrams of simplicial sets, Nederl. Akad. Wetensch. Indag. Math. 46 (1984) 139 MR749527
27	S Eilenberg, S Mac Lane, Cohomology theory of Abelian groups and homotopy theory. I, II, III, Proc. Nat. Acad. Sci. U. S. A. 36, 36, 37 (1950) 443, 657, 307 MR0038072
28	S Eilenberg, S Mac Lane, On the groups of H(Π,n), I, Ann. of Math. 58 (1953) 55 MR0056295
29	S Eilenberg, S Mac Lane, On the groups H(Π,n), II : Methods of computation, Ann. of Math. 60 (1954) 49 MR0065162
30	A Fröhlich, C T C Wall, Graded monoidal categories, Compositio Math. 28 (1974) 229 MR0349804
31	A Fröhlich, C T C Wall, Equivariant Brauer groups, from: "Quadratic forms and their applications (Dublin, 1999)" (editors E Bayer-Fluckiger, D Lewis, A Ranicki), Contemp. Math. 272, Amer. Math. Soc. (2000) 57 MR1803361
32	P Gabriel, M Zisman, Calculus of fractions and homotopy theory, 35, Springer (1967) MR0210125
33	J Giraud, Méthode de la descente, 2, Soc. Math. France (1964) MR0190142
34	J Giraud, Cohomologie non abélienne, 179, Springer (1971) MR0344253
35	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
36	A Grothendieck, Catégories fibrées et déscente, Exp. VI, from: "Séminaire de Géométrie Algébrique du Bois Marie 1960–1961 (SGA 1)", Lecture Notes in Math. 224, Springer (1971) 145 MR0354651
37	A Grothendieck, Techniques de construction et théorèmes d’existence en géométrie algébrique. III : Préschemas quotients, Exp. No. 212, from: "Séminaire Bourbaki, Vol. 6", Soc. Math. France (1995) 99 MR1611786
38	S Hollander, Diagrams indexed by Grothendieck constructions, Homology, Homotopy Appl. 10 (2008) 193 MR2475623
39	S Hollander, A homotopy theory for stacks, Israel J. Math. 163 (2008) 93 MR2391126
40	L Illusie, Complexe cotangent et déformations, II, 283, Springer (1972) MR0491681
41	A Joyal, R Street, Braided tensor categories, Adv. Math. 102 (1993) 20 MR1250465
42	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
43	S Mac Lane, Cohomology theory of Abelian groups, from: "Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, Vol. 2", Amer. Math. Soc. (1952) 8 MR0045115
44	S Mac Lane, Homology, 114, Academic Press (1963) MR0156879
45	S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR0354798
46	B Mitchell, Rings with several objects, Advances in Math. 8 (1972) 1 MR0294454
47	I Moerdijk, J A Svensson, The equivariant Serre spectral sequence, Proc. Amer. Math. Soc. 118 (1993) 263 MR1123662
48	I Moerdijk, J A Svensson, A Shapiro lemma for diagrams of spaces with applications to equivariant topology, Compositio Math. 96 (1995) 249 MR1327146
49	B Noohi, Notes on 2–groupoids, 2–groups and crossed modules, Homology, Homotopy Appl. 9 (2007) 75 MR2280287
50	R J Piacenza, Cohomology of diagrams and equivariant singular theory, Pacific J. Math. 91 (1980) 435 MR615691
51	D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
52	J E Roos, Sur les foncteurs dérivés de . Applications, C. R. Acad. Sci. Paris 252 (1961) 3702 MR0132091
53	N Saavedra Rivano, Catégories Tannakiennes, 265, Springer (1972) MR0338002
54	H X Sinh, Gr–catégories, PhD thesis, Université Paris VII (1975)
55	R Street, Fibrations in bicategories, Cahiers Topologie Géom. Différentielle 21 (1980) 111 MR574662
56	R Street, Categorical structures, from: "Handbook of algebra, Vol. 1" (editor M Hazewinkel), North-Holland (1996) 529 MR1421811
57	D Tamaki, The Grothendieck construction and gradings for enriched categories arXiv:0907.0061
58	A Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory arXiv:math/0412512
59	C E Watts, A homology theory for small categories, from: "Proc. Conf. Categorical Algebra (La Jolla, CA, 1965)" (editors S Eilenberg, D K Harrison, H Röhri, S Mac Lane), Springer (1966) 331 MR0204497
60	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508