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The Baum-Connes conjecture predicts that a certain assembly map is anisomorphism. We identify the homotopy theoretical construction of the assemblymap by Davis and L\"uck with the category theoretical construction by Meyer andNest. This extends the result of Hambleton and Pedersen to arbitrarycoefficients. Our approach uses abstract properties rather than explicitconstructions and is formally similar to Meyer's and Nest's identification oftheir assembly map with the original construction of the assembly map by Baum,Connes and Higson.

An identification of the Baum-Connes and Davis-L\"uck assembly maps