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We provide such a treatment in the framework of universal coalgebra, in which the type of a system (nondeterministic, probabilistic, weighted, game-based etc.) is abstracted as a set functor: We introduce <jats:italic>relational connectors<\/jats:italic> among set functors, which induce notions of heterogeneous (bi)simulation among coalgebras of the respective types. We give a number of constructions on relational connectors. In particular, we identify composition and converse operations on relational connectors; we construct corresponding identity relational connectors, showing that the latter generalize the standard Barr extension of weak-pullback-preserving functors; and we introduce a Kantorovich construction in which relational connectors are induced from relations between modalities. For Kantorovich relational connectors, one has a notion of dual-purpose modal logic interpreted over both system types, and we prove a corresponding Hennessy-Milner-type theorem stating that generalized (bi)similarity coincides with theory inclusion on finitely-branching systems. We apply these results to a number of example scenarios involving labelled transition systems with different label alphabets, probabilistic systems, and input\/output conformances.<\/jats:p>","DOI":"10.1007\/978-3-031-90897-2_6","type":"book-chapter","created":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T08:18:30Z","timestamp":1746001110000},"page":"111-132","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Relational Connectors and Heterogeneous Simulations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8581-0675","authenticated-orcid":false,"given":"Pedro","family":"Nora","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1404-6232","authenticated-orcid":false,"given":"Jurriaan","family":"Rot","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3146-5906","authenticated-orcid":false,"given":"Lutz","family":"Schr\u00f6der","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9796-9675","authenticated-orcid":false,"given":"Paul","family":"Wild","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,1]]},"reference":[{"key":"6_CR1","unstructured":"Ad\u00e1mek, J., Herrlich, H., Strecker, G.E.: Abstract and concrete categories: The joy of cats. 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