Some Models of Heterogeneous and Distributed Specifications based on Universal Constructions

In the last few years, it has been shown that much of the modern architectural software engineering can be suitably modelled with standard tools of category theory. In [9, 20], it is presented how universal constructions (limits and colimits) can, under certain mathematical conditions, help in providing modular tools to interconnect heterogeneous distributed systems described as specifications within arbitrary logical systems. In this paper, we revisit the theme of software interoperability and investigate how to extend these ideas to situations where the mathematical conditions in [9, 20] are not (fully) satisfied.