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 [ W − 1 ] {\displaystyle C[W^{-1}]} of C with respect to W; that is, π 0 L C ( x , y ) = C [ W − 1 ] ( x , y ) {\displaystyle \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.
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 [ W − 1 ] {\displaystyle C[W^{-1}]} of C with respect to W; that is, π 0 L C ( x , y ) = C [ W − 1 ] ( x , y ) {\displaystyle \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.
Source: Wikipedia "Simplicial localization" · CC BY-SA 4.0
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