Volume 21, issue 3 (2021)

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

Volume 23
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

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
$2$–Segal objects and the Waldhausen construction

Julia E Bergner, Angélica M Osorno, Viktoriya Ozornova, Martina Rovelli and Claudia I Scheimbauer

Algebraic & Geometric Topology 21 (2021) 1267–1326
Bibliography
1 D W Anderson, Fibrations and geometric realizations, Bull. Amer. Math. Soc. 84 (1978) 765 MR500935
2 C Barwick, (,n)–Cat as a closed model category, PhD thesis, University of Pennsylvania (2005)
3 C Barwick, On left and right model categories and left and right Bousfield localizations, Homology Homotopy Appl. 12 (2010) 245 MR2771591
4 C Barwick, On the Q construction for exact –categories, preprint (2013) arXiv:1301.4725
5 C Barwick, On the algebraic K–theory of higher categories, J. Topol. 9 (2016) 245 MR3465850
6 J E Bergner, A M Osorno, V Ozornova, M Rovelli, C I Scheimbauer, 2–Segal sets and the Waldhausen construction, Topology Appl. 235 (2018) 445 MR3760213
7 J E Bergner, A M Osorno, V Ozornova, M Rovelli, C I Scheimbauer, Comparison of Waldhausen constructions, preprint (2019) arXiv:1901.03606
8 A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K–theory, Geom. Topol. 17 (2013) 733 MR3070515
9 D Calaque, C Scheimbauer, A note on the (,n)–category of cobordisms, Algebr. Geom. Topol. 19 (2019) 533 MR3924174
10 L Carlier, Incidence bicomodules, Möbius inversion and a Rota formula for infinity adjunctions, Algebr. Geom. Topol. 20 (2020) 169 MR4071369
11 T Dyckerhoff, M Kapranov, Higher Segal spaces, 2244, Springer (2019) MR3970975
12 M Feller, R Garner, J Kock, M U Proulx, M Weber, Every 2–Segal space is unital, Commun. Contemp. Math. 23 (2021) MR4201031
13 T M Fiore, S Paoli, A Thomason model structure on the category of small n–fold categories, Algebr. Geom. Topol. 10 (2010) 1933 MR2728481
14 T M Fiore, S Paoli, D Pronk, Model structures on the category of small double categories, Algebr. Geom. Topol. 8 (2008) 1855 MR2449004
15 T M Fiore, M Pieper, Waldhausen additivity: classical and quasicategorical, J. Homotopy Relat. Struct. 14 (2019) 109 MR3913973
16 I Gálvez-Carrillo, J Kock, A Tonks, Decomposition spaces, incidence algebras and Möbius inversion, I : Basic theory, Adv. Math. 331 (2018) 952 MR3804694
17 M Grandis, R Pare, Limits in double categories, Cahiers Topologie Géom. Différentielle Catég. 40 (1999) 162 MR1716779
18 B J Guillou, J P May, M Merling, A M Osorno, Symmetric monoidal G–categories and their strictification, (2020) MR4077192
19 R Haugseng, Iterated spans and classical topological field theories, Math. Z. 289 (2018) 1427 MR3830256
20 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
21 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
22 L Illusie, Complexe cotangent et déformations, II, 283, Springer (1972) MR0491681
23 A Joyal, Notes on quasi-categories, preprint (2008)
24 A Joyal, M Tierney, Quasi-categories vs Segal spaces, 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) 277 MR2342834
25 G M Kelly, Basic concepts of enriched category theory, 64, Cambridge Univ. Press (1982) 245 MR651714
26 J Lurie, Stable infinity categories, preprint (2006) arXiv:math/0608228
27 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
28 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
29 D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
30 E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
31 B Toën, G Vezzosi, Homotopical algebraic geometry, I : Topos theory, Adv. Math. 193 (2005) 257 MR2137288
32 F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796