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.