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 π 0 is the localization C [ W − 1 ] of C with respect to W; that is, π 0 L C ( x , y ) = C [ W − 1 ] ( x , y ) for any objects x, y in C. The notion is due to Dwyer and Kan.