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 formula_1 is the localization formula_2 of "C" with respect to "W"; that is, formula_3 for any objects "x", "y" in "C". The notion is due to Dwyer and Kan.