Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-29T02:48:21.869Z Has data issue: false hasContentIssue false
  • English
  • Français

Simplicial radditive functors

Published online by Cambridge University Press:  26 April 2010

Vladimir Voevodsky
Vladimir Voevodsky
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton NJ, USA, [email protected]
Get access

Abstract

The simplicial extension of any functor from Sets to Sets which commutes with directed colimits respects weak equivalences. In the present paper we construct a framework which allows one to extend this result to a wide class of model categories and functors between such categories.

Keywords

non-additivederived functorfinitary varietieslocal equivalences
Type
Research Article
Information
Journal of K-Theory , Volume 5 , Issue 2 , April 2010 , pp. 201 - 244
Copyright
Copyright © ISOPP 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Adámek, Jiří and Rosický, Jiří. Locally presentable and accessible categories, London Mathematical Society Lecture Note Series 189. Cambridge University Press, Cambridge, 1994.Google Scholar
2.Beck, Jonathan Mock. Triples, algebras and cohomology. Repr. Theory Appl. Categ., (2):1–59 (electronic), 2003.Google Scholar
3.Beke, Tibor. Sheafifiable homotopy model categories. Math. Proc. Cambridge Philos. Soc. 129(3):447–475, 2000.CrossRefGoogle Scholar
4.Bousfield, A.K. and Kan, D.M.. Homotopy limits, completions and localizations. Lecture Notes in Math. 304. Springer-Verlag, 1972.CrossRefGoogle Scholar
5.Deligne, Pierre. Voevodsky's lectures on motivic cohomology 2000/2001. In Algebraic Topology, Abel Symposia 4, pages 355–409. Springer, 2009.CrossRefGoogle Scholar
6.Gabriel, P. and Zisman, M.. Calculus of fractions and homotopy theory. Springer-Verlag, Berlin, 1967.CrossRefGoogle Scholar
7.Goerss, Paul G. and Jardine, John F.. Simplicial Homotopy Theory. Birkhauser, 1999.CrossRefGoogle Scholar
8.Hirschhorn, Philip S.. Model categories and their localizations, Mathematical Surveys and Monographs 99. American Mathematical Society, Providence, RI, 2003.Google Scholar
9.Hovey, Mark. Model categories. AMS, Providence, RI, 1999.Google Scholar
10.Hovey, Mark. Spectra and symmetric spectra in general model categories. J. Pure Appl. Algebra 165(1):63–127, 2001.CrossRefGoogle Scholar
11.Quillen, D.. Homotopical algebra. Lecture Notes in Math. 43. Springer-Verlag, Berlin, 1973.Google Scholar
12.Swan, Richard G.. Nonabelian homological algebra and K-theory. In Proceedings of symposia in pure mathematics 17, pages 88–123. AMS, Providence, RI, 1970.Google Scholar
13.Weibel, Charles A.. An introduction to homological algebra. Cambridge University Press, Cambridge, 1994.CrossRefGoogle Scholar