|
Complete Segal spaces arising from simplicial categories
Author(s):
Julia
E.
Bergner
Journal:
Trans. Amer. Math. Soc.
361
(2009),
525-546.
MSC (2000):
Primary 55U40;
Secondary 55U35, 18G55, 18G30, 18D20
Posted:
August 18, 2008
MathSciNet review:
2439415
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for homotopy theories. We then give a characterization, up to weak equivalence, of complete Segal spaces arising from these functors.
References:
-
- 1.
- J.E. Bergner, Homotopy fiber products of homotopy theories, in preparation.
- 2.
- J.E. Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058. MR 2276611 (2007i:18014)
- 3.
- J.E. Bergner, Simplicial monoids and Segal categories, Contemp. Math. 431 (2007), 59-83. MR 2342822
- 4.
- J.E. Bergner, A survey of
 -categories, preprint available at math.AT/0610239. - 5.
- J.E. Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397-436. MR 2321038
- 6.
- J.M. Cordier and T. Porter, Vogt's theorem on categories of homotopy coherent diagrams, Math. Proc. Camb. Phil. Soc. (1986), 100, 65-90. MR 838654 (87i:55027)
- 7.
- Daniel Dugger, Universal homotopy theories, Adv. Math. 164 (2001), no. 1, 144-176. MR 1870515 (2002k:18021)
- 8.
- W.G. Dwyer and D.M. Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980), 17-35. MR 578563 (81h:55019)
- 9.
- W.G. Dwyer and D.M. Kan, A classification theorem for diagrams of simplicial sets, Topology 23(1984), 139-155. MR 744846 (86c:55010a)
- 10.
- W.G. Dwyer and D.M. Kan, Equivalences between homotopy theories of diagrams, Algebraic topology and algebraic
 -theory (Princeton, N.J., 1983), 180-205, Ann. of Math. Stud., 113, Princeton Univ. Press, Princeton, NJ, 1987. MR 921478 (89d:55051) - 11.
- W.G. Dwyer and D.M. Kan, Function complexes in homotopical algebra, Topology 19 (1980), 427-440. MR 584566 (81m:55018)
- 12.
- W.G. Dwyer and D.M. Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980), no. 3, 267-284. MR 579087 (81h:55018)
- 13.
- W.G. Dwyer and J. Spalinski, Homotopy theories and model categories, in Handbook of Algebraic Topology, North-Holland, Amsterdam, 1995. MR 1361887 (96h:55014)
- 14.
- P.G. Goerss and J.F. Jardine, Simplicial Homotopy Theory, Progress in Math, vol. 174, Birkhäuser, 1999. MR 1711612 (2001d:55012)
- 15.
- Philip S. Hirschhorn, Model Categories and Their Localizations, Mathematical Surveys and Monographs 99, AMS, 2003. MR 1944041 (2003j:18018)
- 16.
- Mark Hovey, Model Categories, Mathematical Surveys and Monographs, 63. American Mathematical Society 1999. MR 1650134 (99h:55031)
- 17.
- A. Joyal, Simplicial categories vs quasi-categories, in preparation.
- 18.
- A. Joyal, The theory of quasi-categories I, in preparation.
- 19.
- André Joyal and Myles Tierney, Quasi-categories vs Segal spaces, Contemp. Math. 431 (2007), 277-326. MR 2342834
- 20.
- Saunders Mac Lane, Categories for the Working Mathematician, Second Edition, Graduate Texts in Mathematics 5, Springer-Verlag, 1997. MR 1712872 (2001j:18001)
- 21.
- J.P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press, 1967. MR 0222892 (36:5942)
- 22.
- C.L. Reedy, Homotopy theory of model categories, unpublished manuscript, available at http://www-math.mit.edu/
~psh. - 23.
- Charles Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353(3) (2001), 973-1007. MR 1804411 (2002a:55020)
- 24.
- Bertrand Toën, Derived Hall algebras, Duke Math. J. 135, no. 3 (2006), 587-615. MR 2272977 (2007h:18021)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
55U40,
55U35, 18G55, 18G30, 18D20
Retrieve articles in all Journals with
MSC (2000):
55U40,
55U35, 18G55, 18G30, 18D20
Additional Information:
Julia
E.
Bergner
Affiliation:
Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506
Address at time of publication:
Department of Mathematics, University of California, Riverside, Riverside, California 92521
Email:
bergnerj@member.ams.org
DOI:
10.1090/S0002-9947-08-04616-3
PII:
S 0002-9947(08)04616-3
Keywords:
Simplicial categories,
model categories,
complete Segal spaces,
homotopy theories
Received by editor(s):
April 23, 2007
Posted:
August 18, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
