{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T13:54:16Z","timestamp":1761486856858},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2002,9,16]],"date-time":"2002-09-16T00:00:00Z","timestamp":1032134400000},"content-version":"unspecified","delay-in-days":46,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2002,8]]},"abstract":"<jats:p>Frequently, mathematical structures of a certain type and their morphisms fail to form a \ncategory for lack of composability of the morphisms; one example of this problem is the \nclass of probabilistic automata when equipped with morphisms that allow restriction as well \nas relabelling. The proper mathematical framework for this situation is provided by a \ngeneralisation of category theory in the shape of the so-called precategories, which are \nintroduced and studied in this paper. In particular, notions of adjointness, weak adjointness \nand partial adjointness for precategories are presented and justified in detail. \nThis makes it possible to use universal properties as characterisations of well-known basic \nconstructions in the theory of (generative) probabilistic automata: we show that accessible \nautomata and decision trees, respectively, form coreflective subprecategories of the \nprecategory of probabilistic automata. Moreover, the aggregation of two automata is \nidentified as a partial product, whereas restriction and interconnection of automata are \nrecognised as Cartesian lifts.<\/jats:p>","DOI":"10.1017\/s0960129502003614","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T08:50:31Z","timestamp":1032511831000},"page":"481-512","source":"Crossref","is-referenced-by-count":4,"title":["Universal aspects of probabilistic automata"],"prefix":"10.1017","volume":"12","author":[{"given":"LUTZ","family":"SCHR\u00d6DER","sequence":"first","affiliation":[]},{"given":"PAULO","family":"MATEUS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2002,9,16]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129502003614","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T15:33:12Z","timestamp":1554305592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129502003614\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,8]]}},"alternative-id":["S0960129502003614"],"URL":"https:\/\/doi.org\/10.1017\/s0960129502003614","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,8]]}}}