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Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness. When the functor is restricted to some of the categories induced by these conditions, the resulting categories of coalgebras are even complete.<\/jats:p><jats:p>As a practical application, we use these developments in the specification and analysis of non-deterministic hybrid systems, in particular to obtain suitable notions of stability and behaviour.<\/jats:p>","DOI":"10.1017\/s0960129518000269","type":"journal-article","created":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T08:09:30Z","timestamp":1533888570000},"page":"552-587","source":"Crossref","is-referenced-by-count":5,"title":["Limits in categories of Vietoris coalgebras"],"prefix":"10.1017","volume":"29","author":[{"given":"DIRK","family":"HOFMANN","sequence":"first","affiliation":[]},{"given":"RENATO","family":"NEVES","sequence":"additional","affiliation":[]},{"given":"PEDRO","family":"NORA","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,10]]},"reference":[{"key":"S0960129518000269_ref59","first-page":"618","article-title":"An empty inverse limit","volume":"36","author":"Waterhouse","year":"1972","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0960129518000269_ref54","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0224-5"},{"key":"S0960129518000269_ref53","unstructured":"Stauner T. 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