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Joachim Lambek

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Lambek became assistant professor at McGill; he was made a full professor in 1963. He spent his sabbatical year 1965–66 in at the
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Lambek supervised 17 doctoral students, and has 75 doctoral descendants as of 2020. He has over 100 publications listed in the
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Categories and Types in Logic, Language, and Physics: Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday
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Resolution on the Death of Emeritus Professor Joachim (Jim) Lambek, Department of Mathematics and Statistics
1466: 1446: 1441: 860:— (1969). "Deductive systems and categories II. Standard constructions and closed categories". 430:
about integer sequences. In 1963 he published an important result, now known as Lambek's theorem, on
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when in 1995 he contributed "If Hamilton had prevailed: Quaternions in Physics", which exhibited the
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A: Biquaternion Vectorfields over Minkowski's Space B: The Immersibility of a Semigroup into a Group
554:. Seminar lectures given in 1966 in ZĂĽrich. Lecture Notes in Mathematics, No. 24. Berlin, New York: 1249: 389: 265: 1337: 1034: 1004: 849: 819: 766: 728: 404: 334: 1073: 1398: 1227: 1217: 1190: 1082: 1054: 988: 952: 914: 883: 873: 811: 758: 688: 669: 642: 605: 522: 500: 237: 161: 97: 1388: 1327: 1209: 1100: 1095: 1026: 980: 942: 904: 865: 839: 803: 750: 718: 475: 431: 419: 357: 184: 1281: 1000: 964: 926: 778: 656: 619: 584: 563: 542: 514: 1277: 1050: 996: 960: 922: 774: 652: 638: 615: 580: 576: 559: 555: 538: 526: 510: 451: 439: 381: 338: 311: 274: 245: 189: 119: 111: 58: 786: 1362: 594: 531: 303: 1435: 1341: 1038: 947: 909: 853: 739:—; Moser, L. (1954), "Inverse and Complementary Sequences of Natural Numbers", 732: 415: 287: 226: 204: 1008: 1177: 455: 397: 377: 373: 342: 330: 864:. Vol. 86. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 76–122. 628: 494: 1425: 984: 353: 279: 147: 76: 1213: 326: 1402: 1294:
Casadio, Claudia; Coeke, Bob; Moortgat, Michael; Scott, Philip, eds. (2014),
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MĂĽller-Hoissen, Folkert; Pallo, Jean Marcel; Stasheff, Jim, eds. (2012).
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Lambek, Joachim (1951), "The immersibility of a semigroup into a group",
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was published. On the occasion of Lambek's 90th birthday, a collection
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in fall of 1941. In the spring of 1942, he was released and settled in
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From word to sentence: a computational algebraic approach to grammar
302:, where he entered studies at McGill University, graduating with an 1377:"A Module is Flat if and Only if its Character Module is Injective" 1270:
The Lambek Festschrift: mathematical structures in computer science
1231: 1208:. Progress in Mathematics. Vol. 299. Birkhäuser. p. 18. 575:. Lecture Notes in Mathematics. Vol. 177. Berlin, New York: 418:, especially torsion theories, non-commutative localization, and 356:
celebrating Lambek's contributions to mathematical structures in
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characterizing flatness of a module. His more recent work is in
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Torsion theories, additive semantics, and rings of quotients
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had gathered together a group of researchers interested in
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Lambek retired in 1992 but continued his involvement at
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a year later. In 1950, he completed his doctorate under
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Computational Algebraic Approaches to Natural Language
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to express the free-space electromagnetic equations.
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Associahedra, Tamari Lattices and Related Structures
1189:. Faculty of Science: Meeting of Faculty. Montreal: 895:— (1972), "Bicommutators of nice injectives", 462:, as well as for developing the connections between 362:
Categories and Types in Logic, Language, and Physics
195: 183: 167: 153: 143: 125: 103: 93: 83: 65: 40: 21: 593: 530: 442:; his earliest works in this field were probably 225:(5 December 1922 – 23 June 2014) was a Canadian 1314:"The immersibility of a semigroup into a group" 933:— (1972), "Localization and completion", 458:, and a work that has been very influential in 1268:; Scott, P. J.; Seely, R. A. G., eds. (2000), 1121:"The recipients of the Jeffery-Williams Prize" 596:Introduction to Higher Order Categorical Logic 8: 1172: 1170: 392:. The second component was published by the 450:. He is noted, among other things, for the 423: 1361: 1045:Wilson, Robin; Gray, Jeremy, eds. (2001). 29: 18: 1392: 1331: 946: 908: 843: 722: 533:Rings of quotients of rings of functions 158:Department of Mathematics and Statistics 35:Joachim Lambek in Philadelphia, May 2008 1251:An appreciation of Jim Lambek at McGill 1112: 787:"The Mathematics of Sentence Structure" 1143: 1141: 499:(3rd ed.). Blaisdell Publishing. 447: 443: 7: 1457:21st-century Canadian mathematicians 1452:20th-century Canadian mathematicians 935:Journal of Pure and Applied Algebra 323:Institute for Mathematical Research 278:. From there he was interned as an 1462:21st-century German mathematicians 664:Casadio, Claudia; — (2008). 635:Undergraduate Texts in Mathematics 472:Curry–Howard–Lambek correspondence 306:mathematics degree in 1945 and an 268:. He came to England in 1938 as a 116:Curry–Howard–Lambek correspondence 16:Canadian mathematician (1922–2014) 14: 1420:Faculty profile of Joachim Lambek 795:The American Mathematical Monthly 742:The American Mathematical Monthly 372:Lambek's PhD thesis investigated 364:was produced in tribute to him. 1319:Canadian Journal of Mathematics 711:Canadian Journal of Mathematics 627:Anglin, W. S.; — (1995). 422:. One of his earliest papers, 394:Canadian Journal of Mathematics 350:McGill's mathematics department 1381:Canadian Mathematical Bulletin 832:Canadian Mathematical Bulletin 592:—; Scott, P. J. (1986). 1: 1359:Mathematics Genealogy Project 1125:Canadian Mathematical Society 496:Lectures on rings and modules 234:Professor of Pure Mathematics 948:10.1016/0022-4049(72)90011-4 910:10.1016/0021-8693(72)90034-8 862:Lecture Notes in Mathematics 985:10.1515/thli.1979.6.1-3.221 537:. McGill University Press. 468:cartesian closed categories 296:McGill Junior Matriculation 1508: 1487:German emigrants to Canada 1274:Cambridge University Press 1155:. Legacy.com. 27 June 2014 1047:Mathematical Conversations 1018:Mathematical Intelligencer 602:Cambridge University Press 474:). His last works were on 1214:10.1007/978-3-0348-0405-9 552:Completions of categories 493:Lambek, Joachim (2009) . 460:computational linguistics 424:Lambek & Moser (1954) 211: 136: 28: 1492:McGill University alumni 1482:Kindertransport refugees 1075:In Praise of Quaternions 314:becoming McGill's first 1254:. LambekFest. Montreal. 973:Theoretical Linguistics 396:. He later returned to 229:. He was Peter Redpath 1394:10.4153/CMB-1964-021-9 1333:10.4153/CJM-1951-005-8 845:10.4153/CMB-1961-032-6 724:10.4153/CJM-1951-005-8 630:The heritage of Thales 264:, where he attended a 240:, where he earned his 130:Jeffery–Williams Prize 464:typed lambda calculus 1422:at McGill University 637:. Berlin, New York: 428:Lambek–Moser theorem 412:Mathematical Reviews 244:degree in 1950 with 218:Joachim "Jim" Lambek 108:Lambek–Moser theorem 1375:Lambek, J. (1964). 1248:(5 December 1997). 1180:(2 December 2014). 402:Riemann–Silberstein 256:Lambek was born in 1477:Category theorists 1472:Canadian logicians 1428:(80th anniversary) 1031:10.1007/BF03024783 897:Journal of Algebra 870:10.1007/bfb0079385 529:; — (1966). 335:algebraic topology 282:and deported to a 1298:, Springer-Verlag 1223:978-3-0348-0404-2 1191:McGill University 1083:McGill University 1060:978-1-4613-0195-0 879:978-3-540-04605-9 694:978-88-7699-117-2 675:978-88-7699-125-7 648:978-0-387-94544-6 611:978-0-521-35653-4 432:character modules 420:injective modules 238:McGill University 215: 214: 196:Doctoral students 162:McGill University 138:Scientific career 98:McGill University 1499: 1407: 1406: 1396: 1372: 1366: 1365: 1352: 1346: 1345: 1335: 1306: 1300: 1299: 1291: 1285: 1284: 1262: 1256: 1255: 1242: 1236: 1235: 1201: 1195: 1194: 1188: 1174: 1165: 1164: 1162: 1160: 1153:Montreal Gazette 1149:"Joachim Lambek" 1145: 1136: 1135: 1133: 1131: 1117: 1101:Michael K. Brame 1096:Cartesian monoid 1085: 1080: 1064: 1042: 1011: 967: 950: 929: 912: 891: 856: 847: 826: 791: 785:— (1958), 781: 735: 726: 698: 683:— (2008). 679: 660: 623: 599: 588: 571:— (1971). 567: 550:— (1966). 546: 536: 527:Gillman, Leonard 518: 476:pregroup grammar 440:formal languages 358:computer science 318:in mathematics. 284:prison work camp 224: 205:William Schelter 185:Doctoral advisor 179: 72: 51:December 5, 1922 50: 48: 33: 19: 1507: 1506: 1502: 1501: 1500: 1498: 1497: 1496: 1432: 1431: 1426:Lambek festival 1416: 1411: 1410: 1374: 1373: 1369: 1353: 1349: 1308: 1307: 1303: 1293: 1292: 1288: 1264: 1263: 1259: 1244: 1243: 1239: 1224: 1203: 1202: 1198: 1186: 1176: 1175: 1168: 1158: 1156: 1147: 1146: 1139: 1129: 1127: 1119: 1118: 1114: 1109: 1092: 1078: 1067: 1061: 1051:Springer-Verlag 1044: 1014: 970: 932: 894: 880: 859: 829: 808:10.2307/2310058 789: 784: 755:10.2307/2308078 738: 708: 705: 695: 687:. Polimetrica. 682: 676: 668:. Polimetrica. 663: 649: 639:Springer-Verlag 626: 612: 591: 577:Springer-Verlag 570: 556:Springer-Verlag 549: 521: 507: 492: 489: 484: 452:Lambek calculus 388:immersion in a 382:Minkowski space 370: 339:category theory 312:Hans Zassenhaus 275:Kindertransport 254: 246:Hans Zassenhaus 220: 203: 190:Hans Zassenhaus 177: 160: 120:multicategories 112:Lambek calculus 94:Alma mater 79: 74: 70: 61: 52: 46: 44: 36: 24: 17: 12: 11: 5: 1505: 1503: 1495: 1494: 1489: 1484: 1479: 1474: 1469: 1464: 1459: 1454: 1449: 1444: 1434: 1433: 1430: 1429: 1423: 1415: 1414:External links 1412: 1409: 1408: 1387:(2): 237–243. 1367: 1355:Joachim Lambek 1347: 1301: 1286: 1257: 1237: 1222: 1196: 1166: 1137: 1111: 1110: 1108: 1105: 1104: 1103: 1098: 1091: 1088: 1087: 1086: 1065: 1059: 1012: 979:(2): 221–234, 968: 941:(4): 343–370, 930: 892: 878: 857: 838:(3): 295–302, 827: 802:(3): 154–170, 782: 749:(7): 454–458, 736: 704: 701: 700: 699: 693: 680: 674: 661: 647: 624: 610: 589: 568: 547: 519: 505: 488: 485: 483: 482:Selected works 480: 369: 368:Scholarly work 366: 253: 250: 213: 212: 209: 208: 200:Israel Kleiner 197: 193: 192: 187: 181: 180: 171: 165: 164: 155: 151: 150: 145: 141: 140: 134: 133: 127: 123: 122: 105: 104:Known for 101: 100: 95: 91: 90: 85: 81: 80: 75: 73:(aged 91) 67: 63: 62: 53: 42: 38: 37: 34: 26: 25: 23:Joachim Lambek 22: 15: 13: 10: 9: 6: 4: 3: 2: 1504: 1493: 1490: 1488: 1485: 1483: 1480: 1478: 1475: 1473: 1470: 1468: 1465: 1463: 1460: 1458: 1455: 1453: 1450: 1448: 1445: 1443: 1440: 1439: 1437: 1427: 1424: 1421: 1418: 1417: 1413: 1404: 1400: 1395: 1390: 1386: 1382: 1378: 1371: 1368: 1364: 1360: 1356: 1351: 1348: 1343: 1339: 1334: 1329: 1325: 1321: 1320: 1315: 1311: 1305: 1302: 1297: 1290: 1287: 1283: 1279: 1275: 1271: 1267: 1266:Barr, Michael 1261: 1258: 1253: 1252: 1247: 1246:Barr, Michael 1241: 1238: 1233: 1229: 1225: 1219: 1215: 1211: 1207: 1200: 1197: 1192: 1185: 1184: 1179: 1178:Darmon, Henri 1173: 1171: 1167: 1154: 1150: 1144: 1142: 1138: 1126: 1122: 1116: 1113: 1106: 1102: 1099: 1097: 1094: 1093: 1089: 1084: 1077: 1076: 1071: 1070:Barr, Michael 1066: 1062: 1056: 1052: 1048: 1043:Reprinted in 1040: 1036: 1032: 1028: 1024: 1020: 1019: 1013: 1010: 1006: 1002: 998: 994: 990: 986: 982: 978: 974: 969: 966: 962: 958: 954: 949: 944: 940: 936: 931: 928: 924: 920: 916: 911: 906: 902: 898: 893: 889: 885: 881: 875: 871: 867: 863: 858: 855: 851: 846: 841: 837: 833: 828: 825: 821: 817: 813: 809: 805: 801: 797: 796: 788: 783: 780: 776: 772: 768: 764: 760: 756: 752: 748: 744: 743: 737: 734: 730: 725: 720: 716: 712: 707: 706: 702: 696: 690: 686: 681: 677: 671: 667: 662: 658: 654: 650: 644: 640: 636: 632: 631: 625: 621: 617: 613: 607: 603: 598: 597: 590: 586: 582: 578: 574: 569: 565: 561: 557: 553: 548: 544: 540: 535: 534: 528: 524: 520: 516: 512: 508: 506:9780821849002 502: 498: 497: 491: 490: 486: 481: 479: 477: 473: 469: 465: 461: 457: 453: 449: 448:Lambek (1979) 445: 444:Lambek (1958) 441: 437: 433: 429: 426:, proved the 425: 421: 417: 416:module theory 413: 408: 406: 403: 399: 398:biquaternions 395: 391: 387: 384:, as well as 383: 380:algebra over 379: 375: 374:vector fields 367: 365: 363: 359: 355: 351: 346: 344: 340: 336: 332: 328: 324: 319: 317: 313: 309: 305: 301: 297: 293: 289: 288:New Brunswick 285: 281: 277: 276: 271: 267: 263: 259: 251: 249: 247: 243: 239: 235: 232: 228: 227:mathematician 223: 219: 210: 206: 201: 198: 194: 191: 188: 186: 182: 175: 172: 170: 166: 163: 159: 156: 152: 149: 146: 142: 139: 135: 131: 128: 124: 121: 117: 113: 109: 106: 102: 99: 96: 92: 89: 86: 82: 78: 69:June 23, 2014 68: 64: 60: 56: 43: 39: 32: 27: 20: 1384: 1380: 1370: 1350: 1323: 1317: 1309: 1304: 1295: 1289: 1269: 1260: 1250: 1240: 1205: 1199: 1193:. p. 2. 1182: 1157:. 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J. 354:festschrift 280:enemy alien 148:Mathematics 84:Citizenship 1436:Categories 1310:Lambek, J. 1232:2012942603 1159:31 October 1130:1 November 1107:References 376:using the 327:ETH Zurich 47:1922-12-05 1403:0008-4395 1342:124979541 1326:: 34–43. 1068:—; 1039:120099630 993:0301-4428 957:0022-4049 919:0021-8693 903:: 60–73, 888:0075-8434 854:121506469 816:0002-9890 763:0002-9890 733:124979541 717:: 34–43, 436:pregroups 386:semigroup 266:Gymnasium 252:Biography 1312:(1951). 1090:See also 1072:(2013), 1009:62697835 703:Articles 405:bivector 329:, where 300:Montreal 231:Emeritus 88:Canadian 77:MontrĂ©al 1357:at the 1282:1770227 1001:0589163 965:0320047 927:0301052 824:1480361 779:0062777 771:2308078 657:1369087 620:0856915 585:0284459 564:0209330 543:0200747 515:0206032 304:honours 272:on the 270:refugee 262:Germany 258:Leipzig 59:Germany 55:Leipzig 1401:  1340:  1280:  1230:  1220:  1057:  1037:  1007:  999:  991:  963:  955:  925:  917:  886:  876:  852:  822:  814:  777:  769:  761:  731:  691:  672:  655:  645:  618:  608:  583:  562:  541:  513:  503:  292:Canada 207:(1972) 202:(1967) 178:(1950) 176:  169:Thesis 144:Fields 132:(1988) 126:Awards 1338:S2CID 1187:(PDF) 1079:(PDF) 1035:S2CID 1005:S2CID 850:S2CID 820:JSTOR 790:(PDF) 767:JSTOR 729:S2CID 487:Books 470:(see 390:group 1399:ISSN 1228:LCCN 1218:ISBN 1161:2018 1132:2018 1055:ISBN 989:ISSN 953:ISSN 915:ISSN 884:ISSN 874:ISBN 812:ISSN 759:ISSN 689:ISBN 670:ISBN 643:ISBN 606:ISBN 501:ISBN 466:and 446:and 438:and 337:and 222:FRSC 66:Died 41:Born 1389:doi 1328:doi 1210:doi 1027:doi 981:doi 943:doi 905:doi 866:doi 840:doi 804:doi 751:doi 719:doi 325:at 316:PhD 308:MSc 286:in 242:PhD 236:at 1438:: 1397:. 1383:. 1379:. 1336:. 1322:. 1316:. 1278:MR 1276:, 1272:, 1226:. 1216:. 1169:^ 1151:. 1140:^ 1123:. 1081:, 1053:. 1049:. 1033:. 1023:17 1021:. 1003:, 997:MR 995:, 987:, 975:, 961:MR 959:, 951:, 937:, 923:MR 921:, 913:, 901:21 899:, 882:. 872:. 848:, 834:, 818:, 810:, 800:65 798:, 792:, 775:MR 773:, 765:, 757:, 747:61 745:, 727:, 713:, 653:MR 651:. 641:. 633:. 616:MR 614:. 604:. 600:. 581:MR 579:. 560:MR 558:. 539:MR 525:; 511:MR 509:. 478:. 290:, 260:, 118:, 114:, 110:, 57:, 1405:. 1391:: 1385:7 1344:. 1330:: 1324:3 1234:. 1212:: 1163:. 1134:. 1063:. 1041:. 1029:: 983:: 977:6 945:: 939:2 907:: 890:. 868:: 842:: 836:4 806:: 753:: 721:: 715:3 697:. 678:. 659:. 622:. 587:. 566:. 545:. 517:. 49:) 45:(

Index


Leipzig
Germany
Montréal
Canadian
McGill University
Lambek–Moser theorem
Lambek calculus
Curry–Howard–Lambek correspondence
multicategories
Jeffery–Williams Prize
Mathematics
Department of Mathematics and Statistics
McGill University
Thesis
Doctoral advisor
Hans Zassenhaus
Israel Kleiner
William Schelter
FRSC
mathematician
Emeritus
Professor of Pure Mathematics
McGill University
PhD
Hans Zassenhaus
Leipzig
Germany
Gymnasium
refugee

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