{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:40:15Z","timestamp":1777646415541,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-4","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2000,8]]},"abstract":"<jats:p>The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some well-known categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete.<\/jats:p>","DOI":"10.3233\/fi-2000-43123402","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T22:12:28Z","timestamp":1575324748000},"page":"21-48","source":"Crossref","is-referenced-by-count":4,"title":["Finite Completeness of Categories of Petri Nets"],"prefix":"10.1177","volume":"43","author":[{"given":"Marek A.","family":"Bednarczyk","sequence":"first","affiliation":[{"name":"Institute of Computer Science, Gda\u0144sk Branch, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland. email: {m.bednarczyk,a.borzyszkowski}@ipipan.gda.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej M.","family":"Borzyszkowski","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Gda\u0144sk Branch, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland. email: {m.bednarczyk,a.borzyszkowski}@ipipan.gda.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafa\u0142","family":"Somla","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Gda\u0144sk University, Wita Stwosza 57, 80-952 Gda\u0144sk, Poland. email: rsomla@univ.gda.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2000-43123402","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2000-43123402","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:35:10Z","timestamp":1777444510000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2000-43123402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1,1]]},"references-count":0,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2000,8]]}},"alternative-id":["10.3233\/FI-2000-43123402"],"URL":"https:\/\/doi.org\/10.3233\/fi-2000-43123402","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1,1]]}}}