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Canonical Selection of Colimits

Abstract : Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in the specification language CASL), and (2) of combinations of networks of specifications (in the OMG standardised language DOL).The problem of using colimits as the semantics of certain language constructs is that they are defined only up to isomorphism. However, the semantics of a complex specification in these languages is given by a signature and a class of models over that signature – not by an isomorphism class of signatures. This is particularly relevant when a specification with colimit semantics is further translated or refined. The user needs to know the symbols of a signature for writing a correct refinement.Therefore, we study how to usefully choose one representative of the isomorphism class of all colimits of a given diagram. We develop criteria that colimit selections should meet. We work over arbitrary inclusive categories, but start the study how the criteria can be met with $$\mathbb Set$$-like categories, which are often used as signature categories for institutions.
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Till Mossakowski, Florian Rabe, Mihai Codescu. Canonical Selection of Colimits. 23th International Workshop on Algebraic Development Techniques (WADT), Sep 2016, Gregynog, United Kingdom. pp.170-188, ⟨10.1007/978-3-319-72044-9_12⟩. ⟨hal-01767466⟩



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