Volume 17, issue 5 (2017)

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

Volume 21, 1 issue

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
Stable Postnikov data of Picard $2$–categories

Nick Gurski, Niles Johnson, Angélica M Osorno and Marc Stephan

Algebraic & Geometric Topology 17 (2017) 2763–2806
Bibliography
1 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
2 J C Baez, J Dolan, Higher-dimensional algebra, III : n–categories and the algebra of opetopes, Adv. Math. 135 (1998) 145 MR1620826
3 J C Baez, A D Lauda, Higher-dimensional algebra, V : 2–groups, Theory Appl. Categ. 12 (2004) 423 MR2068521
4 B Bartlett, Quasistrict symmetric monoidal 2–categories via wire diagrams, preprint (2014) arXiv:1409.2148v1
5 J Beck, Distributive laws, from: "Seminar on triples and categorical homology theory" (editor B Eckmann), Springer (1969) 119 MR0241502
6 L Bhardwaj, D Gaiotto, A Kapustin, State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter, J. High Energy Phys. (2017) MR3650172
7 R Blackwell, G M Kelly, A J Power, Two-dimensional monad theory, J. Pure Appl. Algebra 59 (1989) 1 MR1007911
8 J Bourke, N Gurski, A cocategorical obstruction to tensor products of Gray-categories, Theory Appl. Categ. 30 (2015) 387 MR3337079
9 J Bourke, N Gurski, The Gray tensor product via factorisation, Appl. Categ. Structures 25 (2017) 603 MR3669174
10 A K Bousfield, E M Friedlander, Homotopy theory of Γ–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
11 R Brown, C B Spencer, G–groupoids, crossed modules and the fundamental groupoid of a topological group, Indag. Math. 38 (1976) 296 MR0419643
12 P Carrasco, A M Cegarra, A R Garzón, Nerves and classifying spaces for bicategories, Algebr. Geom. Topol. 10 (2010) 219 MR2602835
13 E Cheng, N Gurski, The periodic table of n–categories for low dimensions, I : Degenerate categories and degenerate bicategories, from: "Categories in algebra, geometry and mathematical physics" (editors A Davydov, M Batanin, M Johnson, S Lack, A Neeman), Contemp. Math. 431, Amer. Math. Soc. (2007) 143 MR2342826
14 E Cheng, N Gurski, The periodic table of n–categories, II : Degenerate tricategories, Cah. Topol. Géom. Différ. Catég. 52 (2011) 82 MR2839900
15 E Cheng, N Gurski, Iterated icons, Theory Appl. Categ. 29 (2014) 929 MR3294506
16 D Conduché, Modules croisés généralisés de longueur 2, J. Pure Appl. Algebra 34 (1984) 155 MR772056
17 S Eilenberg, S MacLane, On the groups H,n), II : Methods of computation, Ann. of Math. 60 (1954) 49 MR0065163
18 S Eilenberg, S MacLane, On the groups H,n), III : Operations and obstructions, Ann. of Math. 60 (1954) 513 MR0065163
19 D S Freed, Anomalies and invertible field theories, from: "String-Math 2013" (editors R Donagi, M R Douglas, L Kamenova, M Roček), Proc. Sympos. Pure Math. 88, Amer. Math. Soc. (2014) 25 MR3330283
20 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, I, J. Topol. 4 (2011) 737 MR2860342
21 R Gordon, A J Power, R Street, Coherence for tricategories, 558, Amer. Math. Soc. (1995) MR1261589
22 J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
23 A Grothendieck, Pursuing stacks, unpublished manuscript (1983)
24 Z C Gu, X G Wen, Symmetry-protected topological orders for interacting fermions : Fermionic topological nonlinear σ models and a special group supercohomology theory, Phys. Rev. B 90 (2014)
25 N Gurski, Nerves of bicategories as stratified simplicial sets, J. Pure Appl. Algebra 213 (2009) 927 MR2498786
26 N Gurski, Biequivalences in tricategories, Theory Appl. Categ. 26 (2012) 349 MR2972968
27 N Gurski, Coherence in three-dimensional category theory, 201, Cambridge Univ. Press (2013) MR3076451
28 N Gurski, The monoidal structure of strictification, Theory Appl. Categ. 28 (2013) 1 MR3023916
29 N Gurski, N Johnson, A M Osorno, K–theory for 2–categories, preprint (2015) arXiv:1503.07824v1
30 N Gurski, N Johnson, A M Osorno, The 2–dimensional stable homotopy hypothesis, preprint (2017)
31 N Gurski, A M Osorno, Infinite loop spaces, and coherence for symmetric monoidal bicategories, Adv. Math. 246 (2013) 1 MR3091798
32 J F Jardine, Supercoherence, J. Pure Appl. Algebra 75 (1991) 103 MR1138365
33 N Johnson, A M Osorno, Modeling stable one-types, Theory Appl. Categ. 26 (2012) 520 MR2981952
34 A Joyal, R Street, Braided tensor categories, Adv. Math. 102 (1993) 20 MR1250465
35 D W Kahn, The spectral sequence of a Postnikov system, Comment. Math. Helv. 40 (1966) 169 MR0195096
36 M Kapranov, Supergeometry in mathematics and physics, preprint (2015) arXiv:1512.07042v1
37 G M Kelly, Doctrinal adjunction, from: "Category seminar" (editor G M Kelly), Lecture Notes in Math. 420, Springer (1974) 257 MR0360749
38 G M Kelly, R Street, Review of the elements of 2–categories, from: "Category seminar" (editor G M Kelly), Lecture Notes in Math. 420, Springer (1974) 75 MR0357542
39 S Lack, Codescent objects and coherence, J. Pure Appl. Algebra 175 (2002) 223 MR1935980
40 S Lack, A 2–categories companion, from: "Towards higher categories" (editors J C Baez, J P May), IMA Vol. Math. Appl. 152, Springer (2010) 105 MR2664622
41 S Lack, Icons, Appl. Categ. Structures 18 (2010) 289 MR2640216
42 S Lack, S Paoli, 2–nerves for bicategories, K–Theory 38 (2008) 153 MR2366560
43 J L Loday, Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982) 179 MR651845
44 S MacLane, J H C Whitehead, On the 3–type of a complex, Proc. Nat. Acad. Sci. U. S. A. 36 (1950) 41 MR0033519
45 M A Mandell, An inverse K–theory functor, Doc. Math. 15 (2010) 765 MR2735988
46 J P May, E spaces, group completions, and permutative categories, from: "New developments in topology" (editor G Segal), London Math. Soc. Lecture Note Ser. 11, Cambridge Univ. Press (1974) 61 MR0339152
47 J P May, The spectra associated to permutative categories, Topology 17 (1978) 225 MR508886
48 J P May, R Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978) 205 MR508885
49 P McCrudden, Balanced coalgebroids, Theory Appl. Categ. 7 (2000) 71 MR1764504
50 R E Mosher, M C Tangora, Cohomology operations and applications in homotopy theory, Harper & Row (1968) MR0226634
51 A J Power, A general coherence result, J. Pure Appl. Algebra 57 (1989) 165 MR985657
52 C J Schommer-Pries, The classification of two-dimensional extended topological field theories, preprint (2014) arXiv:1112.1000v2
53 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
54 H X Sính, Gr–catégories, PhD thesis, Université Paris VII (1975)
55 R Street, Fibrations in bicategories, Cahiers Topologie Géom. Différentielle 21 (1980) 111 MR574662
56 R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404
57 R W Thomason, Symmetric monoidal categories model all connective spectra, Theory Appl. Categ. 1 (1995) 78 MR1337494
58 J H C Whitehead, Combinatorial homotopy, II, Bull. Amer. Math. Soc. 55 (1949) 453 MR0030760