The assembly allows the fixing of a pulley to a base and comprises a pulley and a support comprising a cylindrical shaft and a connecting element which can be connected to the base. The assembly comprises a support piece with a fixing part with a fixing orifice, and a support part the cylindrical shaft being secured by a second end to the support piece through the fixing orifice, and the support piece being in turn supported by the base through the support part which is designed to rest on the base, so that the cylindrical shaft is supported through its first end joined to the connecting element and its second end through the support piece, and so that the pulley is retained between the base and the support piece.