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We use the fact, from Joyal et al., that coreflections preserve open morphisms situations in the sense that a coreflection induces a path subcategory in the category of systems in such a way that open ... We prove that this method is particularly well-suited for systems with quantitative information: we canonically recover the path category of probabilistic systems from Cheng et al., and of timed systems ... Quantitative bisimulations using coreflections and open morphisms A Omitted proofs from Section 2.4 Proof (of Proposition 3). iii) ⇒ i) Obvious. i) ⇒ ii) Given such a span f : T ′′ −→ T and g : T ...arXiv:1809.09278v1 fatcat:47n4uw6ozfeeffhci47ydoxk6m
in the former higher-order is expressed by passing around syntactic objects (such as terms or processes) as representations of behaviours whereas the former ditches the syntactic encoding altogether and ... As a direct application of the theory of coalgebras, we are now able to define a canonical higher-order coalgebraic bisimulation and show it to coincide with coalgebraic bisimulation for value-passing ... In particular, we expect to be able to define general higher-order trace equivalences and higher-order weak bisimulations by applying the constructions given in [6, 7, 17, 26] . ...arXiv:1602.06221v2 fatcat:fudx2s3ckrbvpmupf22wsc4fke
Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. ... We instantiate our framework to timed transition systems and their quantitative extensions such as timed probabilistic systems. ... Their approach is based on open-maps bisimulation and is limited to non-deterministic timed transition systems. ...arXiv:1711.10233v4 fatcat:raoirjtxhngmnlqqcina3viwaa
(English summary) 2000i:68137 Lasota, Stawomir Coalgebra morphisms subsume open maps. ... (English summary) (see 2000h:68006 ) Cheng, Allan (with Nielsen, Mogens) Open maps, behavioural equivalences, and congruences. ...