Simplicial localization

In category theory, a branch of mathematics, the simplicial localization of a category C with respect to a class W of morphisms of C is a simplicial category LC whose ${\pi }_0$ is the localization $C[W^{-1}]$ of C with respect to W; that is, ${\pi }_{0}LC(x,y)=C[W^{-1}](x,y)$ for any objects x, y in C. The notion is due to Dwyer and Kan.

References

• W. G. Dwyer and Dan Kan, Simplicial localizations of categories Archived 2014-03-24 at the Wayback Machine
• http://math.mit.edu/~mdono/_Juvitop.pdf Archived 2013-11-05 at the Wayback Machine

External links

• simplicial localization at the nLab