The encoding of the second step then made explicit the lexical blow up for the interpretation of the functional symbols of the dependency trees in<cite> (Kallmeyer and Kuhlmann, 2012</cite> )'s construct. It also provides a push out (in the categorical sense) of the two morphisms from the disambiguated derivation trees to the derived trees and to the dependency trees. The diagram is completed with the yield function from the derived trees and from the dependency trees to the string vocabulary.