Abstract
The notion of signature morphism is basic to the theory of institutions. It provides a powerful primitive for the study of specifications, their modularity and their relations in an abstract setting. The notion of derived signature morphism generalises signature morphisms to more complex constructions, where symbols may be mapped not only to symbols, but to arbitrary terms. The purpose of this work is to study derived signature morphisms in an institution-independent way. We will recall and generalize two known approaches to derived signature morphisms, introduce a third one, and discuss their pros and cons. We especially study the existence of colimits of derived signature morphisms. The motivation is to give an independent semantics to the notion of derived signature morphism, query and substitution in the context of the Distributed Ontology, Modeling and Specification Language DOL.
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Notes
- 1.
Cmp. the work on the new OMG standard. Distributed Ontology, Modeling and Specification Language (DOL), see http://ontoiop.org.
- 2.
Such an approach is used by the HDTP framework, described in [23].
- 3.
Simplified version from [23].
- 4.
The category \(\mathbf {Set}\) has all sets as objects and all functions as morphisms.
- 5.
\(\mathbb {CAT}\) is the quasi-category of all categories, where “quasi” means that it lives in a higher set-theoretic universe.
- 6.
The original notion from [4] is a lax variant of this: a morphism \(\rho \rightarrow \rho '\circ (I_2 \cdot \theta )\) is given instead of equality.
- 7.
We give only a brief summary here, simplifying and adapting notation.
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Mossakowski, T., Krumnack, U., Maibaum, T. (2015). What Is a Derived Signature Morphism?. In: Codescu, M., Diaconescu, R., Țuțu, I. (eds) Recent Trends in Algebraic Development Techniques. WADT 2015. Lecture Notes in Computer Science(), vol 9463. Springer, Cham. https://doi.org/10.1007/978-3-319-28114-8_6
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