Algebraic & Geometric Topology Volume 10, issue 1 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

To Appear

Other MSP Journals

Nerves and classifying spaces for bicategories

Pilar Carrasco, Antonio M Cegarra and Antonio R Garzón

Algebraic & Geometric Topology 10 (2010) 219–274

DOI: 10.2140/agt.2010.10.219

Bibliography

1	M Artin, B Mazur, On the van Kampen theorem, Topology 5 (1966) 179 MR0192495
2	I Baković, Grothendieck construction for bicategories, Preprint
3	J Bénabou, Introduction to bicategories, from: "Reports of the Midwest Category Seminar", Springer (1967) 1 MR0220789
4	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
5	L Breen, Théorie de Schreier supérieure, Ann. Sci. École Norm. Sup. $(4)$ 25 (1992) 465 MR1191733
6	M Bullejos, A M Cegarra, On the geometry of $2$–categories and their classifying spaces, $K$–Theory 29 (2003) 211 MR2028502
7	M Bullejos, A M Cegarra, Classifying spaces for monoidal categories through geometric nerves, Canad. Math. Bull. 47 (2004) 321 MR2072592
8	P Carrasco, A M Cegarra, (Braided) tensor structures on homotopy groupoids and nerves of (braided) categorical groups, Comm. Algebra 24 (1996) 3995 MR1414569
9	P Carrasco, A M Cegarra, Schreier theory for central extensions of categorical groups, Comm. Algebra 24 (1996) 4059 MR1414570
10	A M Cegarra, M Bullejos, A R Garzón, Higher-dimensional obstruction theory in algebraic categories, J. Pure Appl. Algebra 49 (1987) 43 MR920515
11	A M Cegarra, A R Garzón, Homotopy classification of categorical torsors, Appl. Categ. Structures 9 (2001) 465 MR1865612
12	A M Cegarra, E Khmaladze, Homotopy classification of graded Picard categories, Adv. Math. 213 (2007) 644 MR2332605
13	A M Cegarra, J Remedios, The relationship between the diagonal and the bar constructions on a bisimplicial set, Topology Appl. 153 (2005) 21 MR2172033
14	A M Cegarra, J Remedios, The behaviour of the $\wwbar W$–construction on the homotopy theory of bisimplicial sets, Manuscripta Math. 124 (2007) 427 MR2357792
15	J W Duskin, Simplicial matrices and the nerves of weak $n$–categories. I. Nerves of bicategories, Theory Appl. Categ. 9 (2001) 198 MR1897816
16	Z Fiedorowicz, Classifying spaces of topological monoids and categories, Amer. J. Math. 106 (1984) 301 MR737777
17	R Garner, N Gurski, The low-dimensional structures that tricategories form, to appear in Mathematical Proc. Camb. Phil. Soc. arXiv:0711.1761
18	P G Glenn, Realization of cohomology classes in arbitrary exact categories, J. Pure Appl. Algebra 25 (1982) 33 MR660389
19	P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Math. 174, Birkhäuser Verlag (1999) MR1711612
20	R Gordon, A J Power, R Street, Coherence for tricategories, Mem. Amer. Math. Soc. 117 (1995) MR1261589
21	A Grothendieck, Catégories fibrées et déscente, from: "Revêtements étales et groupe fondamental", Lecture Notes in Math. 224, Springer (1971) 145 MR0354651
22	N Gurski, An algebraic theory of tricategory, PhD thesis, University of Chicago (2007)
23	N Gurski, Nerves of bicategories as stratified simplicial sets, J. Pure Appl. Algebra 213 (2009) 927 MR2498786
24	V A Hinich, V V Schechtman, Geometry of a category of complexes and algebraic $K$–theory, Duke Math. J. 52 (1985) 399 MR792180
25	J F Jardine, Supercoherence, J. Pure Appl. Algebra 75 (1991) 103 MR1138365
26	A Joyal, R Street, Braided tensor categories, Adv. Math. 102 (1993) 20 MR1250465
27	M M Kapranov, V A Voevodsky, $2$–categories and Zamolodchikov tetrahedra equations, from: "Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991)", Proc. Sympos. Pure Math. 56, Amer. Math. Soc. (1994) 177 MR1278735
28	S Lack, ICONS arXiv:0711.4657
29	S Lack, S Paoli, $2$–nerves for bicategories, $K$–Theory 38 (2008) 153 MR2366560
30	S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
31	J P May, Simplicial objects in algebraic topology, Van Nostrand Math. Studies 11, D Van Nostrand Co. (1967) MR0222892
32	J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
33	J P May, Pairings of categories and spectra, J. Pure Appl. Algebra 19 (1980) 299 MR593258
34	I Moerdijk, J A Svensson, Algebraic classification of equivariant homotopy $2$–types. I, J. Pure Appl. Algebra 89 (1993) 187 MR1239560
35	D Quillen, Higher algebraic $K$–theory. I, from: "Algebraic $K$–theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)", Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
36	G Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. (1968) 105 MR0232393
37	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
38	C Simson, A closed model structure for $n$–categories, internal $hom$, $n$–staks and generalized Seifert–Van Kampen arXiv:9704.5006
39	R Street, Two constructions on lax functors, Cahiers Topologie Géom. Différentielle 13 (1972) 217 MR0347936
40	R Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283 MR920944
41	R Street, Categorical structures, from: "Handbook of algebra, Vol. 1", North-Holland (1996) 529 MR1421811
42	Z Tamsamani, Sur des notions de $n$–catégorie et $n$-groupoïde non strictes via des ensembles multi-simpliciaux, $K$–Theory 16 (1999) 51 MR1673923
43	R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404
44	U Tillmann, Discrete models for the category of Riemann surfaces, Math. Proc. Cambridge Philos. Soc. 121 (1997) 39 MR1418359
45	U Tillmann, On the homotopy of the stable mapping class group, Invent. Math. 130 (1997) 257 MR1474157
46	K Worytkiewicz, K Hess, P E Parent, A Tonks, A model structure à la Thomason on \bf2-Cat, J. Pure Appl. Algebra 208 (2007) 205 MR2269840