Volume 14, issue 4 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Comparing geometric realizations of tricategories

Antonio M Cegarra and Benjamín A Heredia

Algebraic & Geometric Topology 14 (2014) 1997–2064
Bibliography
1 J C Baez, The homotopy hypothesis
2 J C Baez, M Neuchl, Higher-dimensional algebra, I: Braided monoidal $2$–categories, Adv. Math. 121 (1996) 196 MR1402727
3 C Balteanu, Z Fiedorowicz, R Schwänzl, R Vogt, Iterated monoidal categories, Adv. Math. 176 (2003) 277 MR1982884
4 J Bénabou, Introduction to bicategories, from: "Reports of the Midwest Category Seminar", Springer (1967) 1 MR0220789
5 C Berger, Double loop spaces, braided monoidal categories and algebraic $3$–type of space, from: "Higher homotopy structures in topology and mathematical physics", Contemp. Math. 227, Amer. Math. Soc. (1999) 49 MR1665460
6 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics 304, Springer (1972) MR0365573
7 M Bullejos, A M Cegarra, On the geometry of $2$–categories and their classifying spaces, $K\!$–Theory 29 (2003) 211 MR2028502
8 M Bullejos, A M Cegarra, Classifying spaces for monoidal categories through geometric nerves, Canad. Math. Bull. 47 (2004) 321 MR2072592
9 P Carrasco, A M Cegarra, (Braided) tensor structures on homotopy groupoids and nerves of (braided) categorical groups, Comm. Algebra 24 (1996) 3995 MR1414569
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, A R Garzón, Homotopy classification of categorical torsors, Appl. Categ. Structures 9 (2001) 465 MR1865612
14 A M Cegarra, E Khmaladze, Homotopy classification of graded Picard categories, Adv. Math. 213 (2007) 644 MR2332605
15 E Cheng, N Gurski, The periodic table of $n$–categories for low dimensions II: Degenerate tricategories, arXiv:0706.2307
16 J W Duskin, Simplicial matrices and the nerves of weak $n$–categories. I: Nerves of bicategories, Theory Appl. Categ. 9 (2002) 198 MR1897816
17 Z Fiedorowicz, The symmetric bar construction (1998)
18 R Garner, N Gurski, The low-dimensional structures formed by tricategories, Math. Proc. Cambridge Philos. Soc. 146 (2009) 551 MR2496344
19 P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser (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 descente, from: "Séminaire de géométrie algébrique du Bois Marie 1966/67" (editors P Berthelot, A Grothendieck, L Illusie), Lecture Notes in Math. 224, Springer (1971) 145
22 N Gurski, Nerves of bicategories as stratified simplicial sets, J. Pure Appl. Algebra 213 (2009) 927 MR2498786
23 N Gurski, Loop spaces, and coherence for monoidal and braided monoidal bicategories, Adv. Math. 226 (2011) 4225 MR2770448
24 N Gurski, Biequivalences in tricategories, Theory Appl. Categ. 26 (2012) 349 MR2972968
25 N Gurski, Coherence in three-dimensional category theory, Cambridge Tracts in Mathematics 201, Cambridge Univ. Press (2013) MR3076451
26 K A Hardie, K H Kamps, R W Kieboom, A homotopy bigroupoid of a topological space, Appl. Categ. Structures 9 (2001) 311 MR1836257
27 L Illusie, Complexe cotangent et déformations, II, Lecture Notes in Mathematics 283, Springer (1972) MR0491681
28 J F Jardine, Supercoherence, J. Pure Appl. Algebra 75 (1991) 103 MR1138365
29 A Joyal, R Street, Braided tensor categories, Adv. Math. 102 (1993) 20 MR1250465
30 A Joyal, M Tierney, Algebraic homotopy types, Handwritten lecture notes (1984)
31 M M Kapranov, V A Voevodsky, $2$–categories and Zamolodchikov tetrahedra equations, from: "Algebraic groups and their generalizations: quantum and infinite-dimensional methods" (editors W J Haboush, B J Parshall), Proc. Sympos. Pure Math. 56, Amer. Math. Soc. (1994) 177 MR1278735
32 S Lack, Icons, Appl. Categ. Structures 18 (2010) 289 MR2640216
33 S Lack, A Quillen model structure for Gray-categories, J. $K\!$–Theory 8 (2011) 183 MR2842929
34 S Lack, S Paoli, $2$–nerves for bicategories, $K\!$–Th. 38 (2008) 153 MR2366560
35 O Leroy, Sur une notion de $3$–catégorie adaptée à l'homotopie (1994)
36 J P May, The spectra associated to permutative categories, Topology 17 (1978) 225 MR508886
37 D Quillen, Higher algebraic $K\!$–theory, I, from: "Algebraic $K\!$–theory, I: Higher $K\!$–theories", Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
38 G Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. (1968) 105 MR0232393
39 G Segal, Categories and cohomology theories, Topol. 13 (1974) 293 MR0353298
40 C Simpson, Homotopy theory of higher categories, New Mathematical Monographs 19, Cambridge Univ. Press (2012) MR2883823
41 J D Stasheff, Homotopy associativity of $H$–spaces, I, II, Trans. Amer. Math. Soc. 108 (1963) 293 MR0158400
42 D Stevenson, The geometry of bundle gerbes, PhD thesis, University of Adelaide (2000)
43 R Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283 MR920944
44 R Street, Categorical structures, from: "Handbook of algebra, Vol. 1" (editor M Hazewinkel), Handb. Algebr. 1, Elsevier/North-Holland (1996) 529 MR1421811
45 R Street, Categorical and combinatorial aspects of descent theory, Appl. Categ. Structures 12 (2004) 537 MR2107402
46 Z Tamsamani, Sur des notions de $n$–catégorie et $n$–groupoïde non strictes via des ensembles multi-simpliciaux, $K\!$–Theory 16 (1999) 51 MR1673923
47 R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404