{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T03:05:33Z","timestamp":1696993533045},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2023,6]]},"abstract":"Abstract<\/jats:title>We exhibit a bridge between the theory of cellular categories<\/jats:italic>, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence<\/jats:italic>. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin\u2013Eklof\u2013Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosick\u00fd.<\/jats:p>","DOI":"10.1017\/jsl.2022.40","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T09:15:46Z","timestamp":1652865346000},"page":"811-834","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["CELLULAR CATEGORIES AND STABLE INDEPENDENCE"],"prefix":"10.1017","volume":"88","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-7602-0698","authenticated-orcid":false,"given":"MICHAEL","family":"LIEBERMAN","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9733-1222","authenticated-orcid":false,"given":"JI\u0158\u00cd","family":"ROSICK\u00dd","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-2478-6813","authenticated-orcid":false,"given":"SEBASTIEN","family":"VASEY","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,5,18]]},"reference":[{"key":"S0022481222000408_r5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0081346"},{"key":"S0022481222000408_r25","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082243"},{"key":"S0022481222000408_r3","volume-title":"Categoricity","volume":"50","author":"Baldwin","year":"2009"},{"key":"S0022481222000408_r11","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8343"},{"key":"S0022481222000408_r18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760649"},{"key":"S0022481222000408_r12","doi-asserted-by":"publisher","DOI":"10.1515\/9783110803662"},{"key":"S0022481222000408_r2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600579"},{"key":"S0022481222000408_r15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2020.05.036"},{"key":"S0022481222000408_r26","volume-title":"Classification Theory for Abstract Elementary Classes","volume":"18","author":"Shelah","year":"2009"},{"key":"S0022481222000408_r6","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100004722"},{"key":"S0022481222000408_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.06.003"},{"key":"S0022481222000408_r17","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-020-2018-8"},{"key":"S0022481222000408_r19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2014.01.005"},{"key":"S0022481222000408_r27","unstructured":"[27] Vasey, S. , Accessible categories, set theory, and model theory: An invitation, preprint, 2020, arXiv:1904.11307."},{"key":"S0022481222000408_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2016.03.004"},{"key":"S0022481222000408_r10","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-006-1977-x"},{"key":"S0022481222000408_r14","doi-asserted-by":"publisher","DOI":"10.1112\/topo.12011"},{"key":"S0022481222000408_r1","unstructured":"[1] Ad\u00e1mek, J. , Herrlich, H. , and Strecker, G. E. , Abstract and concrete categories, online edition, 2004, available from http:\/\/katmat.math.uni-bremen.de\/acc\/."},{"key":"S0022481222000408_r8","doi-asserted-by":"publisher","DOI":"10.1017\/S0024609301008104"},{"key":"S0022481222000408_r4","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2007.06.003"},{"key":"S0022481222000408_r20","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.12.012"},{"key":"S0022481222000408_r13","unstructured":"[13] Henry, S. , Minimal model structures, preprint, 2020, arXiv:2011.13408."},{"key":"S0022481222000408_r21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(72)90010-2"},{"key":"S0022481222000408_r16","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2019.02.018"},{"key":"S0022481222000408_r22","doi-asserted-by":"crossref","unstructured":"[22] Rosick\u00fd, J. , Accessible categories, saturation and categoricity, this Journal, vol. 62 (1997), no. 3, pp. 891\u2013901.","DOI":"10.2307\/2275577"},{"key":"S0022481222000408_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(02)00043-1"},{"key":"S0022481222000408_r24","volume-title":"Classification Theory and the Number of Non-Isomorphic Models","volume":"92","author":"Shelah","year":"1978"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481222000408","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T06:43:42Z","timestamp":1685083422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481222000408\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,18]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["S0022481222000408"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2022.40","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,18]]},"assertion":[{"value":"\u00a9 The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}