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In this paper we address interoperability between components specified using various languages within a same family of DSLs. Our approach consists in applying results of the category theory in order to merge the languages into a unification one, automatically obtained. For this, we use the category of formal specifications of each DSL in the family. Using colimits on the category of algebraic specifications that implements the semantics of the DSLs in the family, we construct a language that unifies the family. Additionally we obtain translation morphisms from individual DSLs to the resulting unified one. By application of the translation morphisms, one can translate each component specifications into a specification written in the unification language. Moreover, properties established in the context of a DSL are transferred to the unifying language. In this paper, we illustrate the unification and the preservation of a property on an example.