{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:11:31Z","timestamp":1760202691949,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662466773"},{"type":"electronic","value":"9783662466780"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-662-46678-0_6","type":"book-chapter","created":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T09:42:21Z","timestamp":1427881341000},"page":"87-101","source":"Crossref","is-referenced-by-count":4,"title":["States of Convex Sets"],"prefix":"10.1007","author":[{"given":"Bart","family":"Jacobs","sequence":"first","affiliation":[]},{"given":"Bas","family":"Westerbaan","sequence":"additional","affiliation":[]},{"given":"Bram","family":"Westerbaan","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"6_CR1","volume-title":"Convexity Theory and its Applications in Functional Analysis","author":"L. Asimow","year":"1980","unstructured":"Asimow, L., Ellis, A.: Convexity Theory and its Applications in Functional Analysis. Academic Press, New York (1980)"},{"key":"6_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-0021-0","volume-title":"Toposes, triples and theories","author":"M. Barr","year":"1985","unstructured":"Barr, M., Wells, C.: Toposes, triples and theories, vol.\u00a0278. Springer, New York (1985)"},{"key":"6_CR3","doi-asserted-by":"crossref","unstructured":"Barnum, H., Wilce, A.: Information processing in convex operational theories. In: Coecke, B., Mackie, I., Panangaden, P., Selinger, P. (eds.) Proceedings of QPL\/DCM 2008. Elect. Notes in Theor. Comp. Sci, vol. 270(2), pp. 3\u201315. Elsevier, Amsterdam (2008)","DOI":"10.1016\/j.entcs.2011.01.002"},{"key":"6_CR4","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1017\/S1446788700017973","volume":"30","author":"J. Flood","year":"1981","unstructured":"Flood, J.: Semiconvex geometry. Journal of the Australiam Mathematical Society\u00a030, 496\u2013510 (1981)","journal-title":"Journal of the Australiam Mathematical Society"},{"key":"6_CR5","unstructured":"Fritz, T.: Convex spaces I: Definition and examples. arXiv preprint arXiv:0903.5522 (2009)"},{"issue":"3","key":"6_CR6","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/BF01645250","volume":"29","author":"S. Gudder","year":"1973","unstructured":"Gudder, S.: Convex structures and operational quantum mechanics. Communic. Math. Physics\u00a029(3), 249\u2013264 (1973)","journal-title":"Communic. Math. Physics"},{"issue":"2","key":"6_CR7","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1137\/1019038","volume":"19","author":"S. Gudder","year":"1977","unstructured":"Gudder, S.: Convexity and mixtures. Siam Review\u00a019(2), 221\u2013240 (1977)","journal-title":"Siam Review"},{"key":"6_CR8","first-page":"12","volume":"10","author":"T. Heinosaari","year":"2012","unstructured":"Heinosaari, T., Ziman, M.: The mathematical language of quantum theory: from uncertainty to entanglement. AMC\u00a010, 12 (2012)","journal-title":"AMC"},{"key":"6_CR9","series-title":"IFIP AICT","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-15240-5_1","volume-title":"Theoretical Computer Science","author":"B. Jacobs","year":"2010","unstructured":"Jacobs, B.: Convexity, duality and effects. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol.\u00a0323, pp. 1\u201319. Springer, Heidelberg (2010)"},{"key":"6_CR10","doi-asserted-by":"crossref","unstructured":"Jacobs, B.: New directions in categorical logic, for classical, probabilistic and quantum logic. arXiv preprint arXiv:1205.3940v3 (2014)","DOI":"10.2168\/LMCS-11(3:24)2015"},{"key":"6_CR11","doi-asserted-by":"crossref","first-page":"161","DOI":"10.7146\/math.scand.a-11042","volume":"29","author":"A. Kock","year":"1971","unstructured":"Kock, A.: Bilinearity and cartesian closed monads. Mathematica Scandinavica\u00a029, 161\u2013174 (1971)","journal-title":"Mathematica Scandinavica"},{"issue":"04","key":"6_CR12","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1017\/S1446788700010272","volume":"12","author":"A. Kock","year":"1971","unstructured":"Kock, A.: Closed categories generated by commutative monads. Journal of the Australian Mathematical Society\u00a012(04), 405\u2013424 (1971)","journal-title":"Journal of the Australian Mathematical Society"},{"issue":"1","key":"6_CR13","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/BF01220869","volume":"21","author":"W.D. Neumann","year":"1970","unstructured":"Neumann, W.D.: On the quasivariety of convex subsets of affine spaces. Archiv der Mathematik\u00a021(1), 11\u201316 (1970)","journal-title":"Archiv der Mathematik"},{"key":"6_CR14","unstructured":"\u015awirszcz, T.: Monadic functors and categories of convex sets. PhD thesis, Polish Academy of Sciences (1974)"},{"issue":"1","key":"6_CR15","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF02413910","volume":"29","author":"M. Stone","year":"1949","unstructured":"Stone, M.: Postulates for the barycentric calculus. Annali di Matematica Pura ed Applicata\u00a029(1), 25\u201330 (1949)","journal-title":"Annali di Matematica Pura ed Applicata"}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-46678-0_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T23:29:38Z","timestamp":1558308578000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-46678-0_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662466773","9783662466780"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-46678-0_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]}}}