Simplicial localization

Short description: Category theory

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 [math]\displaystyle{ \pi_0 }[/math] is the localization [math]\displaystyle{ C[W^{-1}] }[/math] of C with respect to W; that is, [math]\displaystyle{ \pi_0 LC(x, y) = C[W^{-1}](x, y) }[/math] 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
• http://math.mit.edu/~mdono/_Juvitop.pdf

External links

• simplicial localization in nLab