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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 {\displaystyle \pi _{0}} is the localization C {\displaystyle C} of C with respect to W; that is, π 0 L C = C {\displaystyle \pi _{0}LC=C} for any objects x, y in C. The notion is due to Dwyer and Kan.
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