“Weak consistency” refers to a family of properties concerning the state of a distributed system. One of the key issues in their description is the way in which systems are specified. In this regard, a major advance is represented by the introduction of Replicated Data Types (rdts), in which the meaning of operators is given in terms of two relations, namely, visibility and arbitration. Concretely, a data type operation is defined as a function that maps visibility and arbitration into a return value. In this paper we recast such standard approaches into a denotational framework in which a data type is seen as a function that maps visibility into admissible arbitrations. This characterisation provides a more abstract view of RDTs that (i) highlights some of the implicit assumptions shared in operational approaches to specification; (ii) accommodates underspecification and refinement; (iii) enables a categorical presentation of RDT and the development of composition operators for specifications.