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Category:Category theory

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theory that deals in an abstract way with mathematical structures and relationships between them.
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This category has the following 20 subcategories, out of 20 total.
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The following 189 pages are in this category, out of 189 total.
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Timeline of category theory and related mathematics
8: 1092:Grothendieck's relative point of view 896:Duality theory for distributive lattices 729:Categories for the Working Mathematician 564:This list may not reflect recent changes 677:Brown's representability theorem 7: 559:Pages in category "Category theory" 1250:Lawvere's fixed-point theorem 568: 519: 495: 471: 394: 370: 333: 296: 220: 176: 166: 158: 14: 1087:Grothendieck's Galois theory 18: 1475:Quotient of an abelian category 1280:Limit and colimit of presheaves 1134:Hylomorphism (computer science) 1549:Simplicially enriched category 1201:Isomorphism-closed subcategory 794:Completions in category theory 667:Beck's monadicity theorem 620:Tame abstract elementary class 1: 714:Categorical quantum mechanics 237:Categories in category theory 1492:Refinement (category theory) 943:Esquisse d'un Programme 789:Compact object (mathematics) 1047:Generator (category theory) 744:Category of representations 699:Cartesian monoidal category 593:Glossary of category theory 1717: 1696:Fields of abstract algebra 1559:Skeleton (category theory) 1519:Seifert–Van Kampen theorem 1302:Mac Lane coherence theorem 1285:Localization of a category 1260:Lax natural transformation 1124:Homotopy colimit and limit 1119:Higher-dimensional algebra 1015:List of types of functions 933:Envelope (category theory) 598:Outline of category theory 32:The main article for this 31: 1666:Weak factorization system 1504:Section (category theory) 1393:Point-surjective morphism 1077:Grothendieck construction 1000:Finitely generated object 938:Equivalence of categories 913:Element (category theory) 799:Compositional game theory 615:Abstract elementary class 475:Objects (category theory) 418:Lemmas in category theory 320:Free algebraic structures 1589:Structural Ramsey theory 1228:Kernel (category theory) 1042:Generalized metric space 834:Cosmos (category theory) 749:Center (category theory) 431:Limits (category theory) 1691:Mathematical structures 1544:Simplicial localization 1539:Sieve (category theory) 1433:Pseudo-abelian category 1413:Polygraph (mathematics) 1339:Nerve (category theory) 1317:Monad (category theory) 1146:Image (category theory) 1032:Gabriel–Popescu theorem 908:Eckmann–Hilton argument 709:Categorical probability 650:Applied category theory 1701:Functions and mappings 1579:Stable module category 1290:Localizing subcategory 1238:Krull–Schmidt category 1213:K-theory of a category 948:Essential monomorphism 891:Dual (category theory) 809:Cone (category theory) 719:Categorical set theory 672:Bousfield localization 640:Allegory (mathematics) 588:Category (mathematics) 357:Higher category theory 1672:Well-pointed category 1574:Stable model category 1171:Injective cogenerator 1082:Grothendieck universe 1072:Grothendieck category 881:Distributive category 861:Descent (mathematics) 543:Category theory stubs 1631:Topological category 1564:Sketch (mathematics) 1465:Quiver (mathematics) 1388:Permutation category 1161:Induced homomorphism 980:Factorization system 814:Conservative functor 682:Bundle (mathematics) 398:Information geometry 1660:Waldhausen category 1609:Symplectic category 1584:Stack (mathematics) 1344:Nodal decomposition 1307:Mathematical object 1233:Krohn–Rhodes theory 1156:Indiscrete category 784:Commutative diagram 764:Coherence condition 630:Accessible category 451:Monoidal categories 374:Homological algebra 200:Additive categories 1648:Universal property 1604:Subterminal object 1569:Spherical category 1403:Pointless topology 1270:Lift (mathematics) 1052:Giraud subcategory 958:Extensive category 250:Category theorists 26:Mathematics portal 1470:Quotient category 1371:Opposite category 1196:Isomorphism class 1186:Internal category 1181:Inserter category 995:Filtered category 928:Enriched category 923:Endomorphism ring 844:Cotriple homology 839:Cotangent complex 804:Concrete category 724:Categorical trace 687:Burnside category 662:Balanced category 635:Adhesive category 625:Abstract nonsense 283:Dagger categories 263:Closed categories 224:Categorical logic 1708: 1668: 1636:Tower of objects 1428:Projective cover 1423:Product category 1418:Posetal category 1275:Lifting property 1223:Karoubi envelope 1176:Injective object 1151:Indexed category 953:Exact completion 871:Dialectica space 866:Diagonal functor 739:Category algebra 734:Categorification 548: 528: 521: 504: 497: 480: 473: 456: 436: 423: 403: 396: 379: 372: 362: 342: 335: 325: 305: 300:Duality theories 298: 288: 268: 255: 242: 229: 222: 205: 185: 178: 28: 23: 22: 1716: 1715: 1711: 1710: 1709: 1707: 1706: 1705: 1681: 1680: 1679: 1678: 1677: 1676: 1664: 1652: 1640: 1613: 1496: 1479: 1447: 1443:Pulation square 1380: 1348: 1331: 1294: 1242: 1205: 1166:Initial algebra 1138: 1106: 1102:Groupoid object 1067:Graded category 1024: 1020:Fusion category 990:Fibred category 962: 900: 886:Double groupoid 856:Day convolution 848: 759:Codensity monad 691: 654: 602: 580: 576:Category theory 556: 555: 554: 553: 550: 549: 533: 530: 529: 518: 509: 506: 505: 494: 485: 482: 481: 470: 461: 458: 457: 441: 438: 437: 425: 424: 408: 405: 404: 393: 384: 381: 380: 369: 364: 363: 347: 344: 343: 332: 327: 326: 310: 307: 306: 295: 290: 289: 273: 270: 269: 257: 256: 244: 243: 231: 230: 219: 210: 207: 206: 190: 187: 186: 175: 157: 156: 155: 154: 60: 46:Category theory 43: 39:Category theory 24: 17: 12: 11: 5: 1714: 1712: 1704: 1703: 1698: 1693: 1683: 1682: 1675: 1674: 1669: 1662: 1656: 1653: 1651: 1650: 1644: 1641: 1639: 1638: 1633: 1628: 1623: 1617: 1614: 1612: 1611: 1606: 1601: 1596: 1591: 1586: 1581: 1576: 1571: 1566: 1561: 1556: 1551: 1546: 1541: 1536: 1531: 1526: 1521: 1516: 1511: 1509:Segal category 1506: 1500: 1497: 1495: 1494: 1489: 1483: 1480: 1478: 1477: 1472: 1467: 1462: 1457: 1451: 1448: 1446: 1445: 1440: 1435: 1430: 1425: 1420: 1415: 1410: 1405: 1400: 1395: 1390: 1384: 1381: 1379: 1378: 1373: 1368: 1363: 1358: 1352: 1349: 1347: 1346: 1341: 1335: 1332: 1330: 1329: 1324: 1319: 1314: 1312:Model category 1309: 1304: 1298: 1295: 1293: 1292: 1287: 1282: 1277: 1272: 1267: 1262: 1257: 1252: 1246: 1243: 1241: 1240: 1235: 1230: 1225: 1220: 1215: 1209: 1206: 1204: 1203: 1198: 1193: 1191:Isbell duality 1188: 1183: 1178: 1173: 1168: 1163: 1158: 1153: 1148: 1142: 1139: 1137: 1136: 1131: 1129:Hopfian object 1126: 1121: 1116: 1110: 1107: 1105: 1104: 1099: 1094: 1089: 1084: 1079: 1074: 1069: 1064: 1059: 1054: 1049: 1044: 1039: 1034: 1028: 1025: 1023: 1022: 1017: 1012: 1007: 1002: 997: 992: 987: 982: 977: 972: 966: 963: 961: 960: 955: 950: 945: 940: 935: 930: 925: 920: 915: 910: 904: 901: 899: 898: 893: 888: 883: 878: 873: 868: 863: 858: 852: 849: 847: 846: 841: 836: 831: 826: 821: 816: 811: 806: 801: 796: 791: 786: 781: 776: 771: 766: 761: 756: 751: 746: 741: 736: 731: 726: 721: 716: 711: 706: 701: 695: 692: 690: 689: 684: 679: 674: 669: 664: 658: 655: 653: 652: 647: 642: 637: 632: 627: 622: 617: 612: 606: 603: 601: 600: 595: 590: 584: 581: 579: 578: 572: 570: 569: 560: 557: 552: 551: 541: 540: 537: 534: 532: 531: 517: 516: 513: 510: 508: 507: 493: 492: 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1484: 1481: 1476: 1473: 1471: 1468: 1466: 1463: 1461: 1458: 1456: 1453: 1452: 1449: 1444: 1441: 1439: 1438:Pseudoalgebra 1436: 1434: 1431: 1429: 1426: 1424: 1421: 1419: 1416: 1414: 1411: 1409: 1406: 1404: 1401: 1399: 1396: 1394: 1391: 1389: 1386: 1385: 1382: 1377: 1374: 1372: 1369: 1367: 1364: 1362: 1359: 1357: 1354: 1353: 1350: 1345: 1342: 1340: 1337: 1336: 1333: 1328: 1327:Multicategory 1325: 1323: 1320: 1318: 1315: 1313: 1310: 1308: 1305: 1303: 1300: 1299: 1296: 1291: 1288: 1286: 1283: 1281: 1278: 1276: 1273: 1271: 1268: 1266: 1263: 1261: 1258: 1256: 1253: 1251: 1248: 1247: 1244: 1239: 1236: 1234: 1231: 1229: 1226: 1224: 1221: 1219: 1218:Kan extension 1216: 1214: 1211: 1210: 1207: 1202: 1199: 1197: 1194: 1192: 1189: 1187: 1184: 1182: 1179: 1177: 1174: 1172: 1169: 1167: 1164: 1162: 1159: 1157: 1154: 1152: 1149: 1147: 1144: 1143: 1140: 1135: 1132: 1130: 1127: 1125: 1122: 1120: 1117: 1115: 1112: 1111: 1108: 1103: 1100: 1098: 1095: 1093: 1090: 1088: 1085: 1083: 1080: 1078: 1075: 1073: 1070: 1068: 1065: 1063: 1060: 1058: 1055: 1053: 1050: 1048: 1045: 1043: 1040: 1038: 1035: 1033: 1030: 1029: 1026: 1021: 1018: 1016: 1013: 1011: 1008: 1006: 1005:Fraïssé limit 1003: 1001: 998: 996: 993: 991: 988: 986: 985:Fiber functor 983: 981: 978: 976: 973: 971: 968: 967: 964: 959: 956: 954: 951: 949: 946: 944: 941: 939: 936: 934: 931: 929: 926: 924: 921: 919: 916: 914: 911: 909: 906: 905: 902: 897: 894: 892: 889: 887: 884: 882: 879: 877: 874: 872: 869: 867: 864: 862: 859: 857: 854: 853: 850: 845: 842: 840: 837: 835: 832: 830: 827: 825: 824:Corestriction 822: 820: 817: 815: 812: 810: 807: 805: 802: 800: 797: 795: 792: 790: 787: 785: 782: 780: 777: 775: 772: 770: 767: 765: 762: 760: 757: 755: 752: 750: 747: 745: 742: 740: 737: 735: 732: 730: 727: 725: 722: 720: 717: 715: 712: 710: 707: 705: 702: 700: 697: 696: 693: 688: 685: 683: 680: 678: 675: 673: 670: 668: 665: 663: 660: 659: 656: 651: 648: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 607: 604: 599: 596: 594: 591: 589: 586: 585: 582: 577: 574: 573: 571: 567: 565: 558: 544: 539: 538: 535: 524: 520: 515: 514: 511: 500: 496: 491: 490: 487: 476: 472: 467: 466: 463: 452: 447: 446: 443: 432: 427: 419: 414: 413: 410: 399: 395: 390: 389: 386: 375: 371: 366: 358: 353: 352: 349: 338: 334: 329: 321: 316: 315: 312: 301: 297: 292: 284: 279: 278: 275: 264: 259: 251: 246: 238: 233: 225: 221: 216: 215: 212: 201: 196: 195: 192: 181: 177: 172: 171: 169: 165: 161:Subcategories 160: 151: 148: 145: 142: 139: 136: 133: 130: 127: 124: 121: 118: 115: 112: 109: 106: 103: 100: 97: 94: 91: 88: 85: 82: 79: 76: 73: 71: 68: 66: 63: 62: 57: 53: 51: 47: 41: 40: 35: 27: 21: 16: 1554:Size functor 1529:Semigroupoid 1376:Overcategory 1062:Globular set 1037:Gamma-object 704:Catamorphism 610:AB5 category 561: 523:Topos theory 499:Sheaf theory 378:(7 C, 126 P) 163: 50:mathematical 45: 44: 37: 1621:T-structure 1599:Subquotient 1594:Subcategory 1514:Segal space 1487:R-algebroid 1398:Pointed set 1255:Lax functor 1010:Freyd cover 975:F-coalgebra 819:Corecursion 774:Coinduction 645:Anamorphism 527:(1 C, 17 P) 503:(2 C, 57 P) 479:(1 C, 13 P) 341:(2 C, 40 P) 304:(4 C, 69 P) 184:(3 C, 29 P) 1685:Categories 1460:Quantaloid 1455:Q-category 1265:Lie operad 1057:Giry monad 402:(1 C, 5 P) 228:(1 C, 7 P) 970:F-algebra 918:Embedding 754:Chu space 180:Morphisms 58:Contents 1114:H-object 1097:Groupoid 876:DisCoCat 779:Cokernel 337:Functors 34:category 1366:Opetope 829:Cosheaf 769:Coimage 1534:Setoid 1408:Polyad 1361:Operad 1322:Monoid 547:(89 P) 455:(40 P) 435:(15 P) 361:(32 P) 324:(25 P) 254:(39 P) 241:(56 P) 204:(14 P) 422:(8 P) 287:(6 P) 267:(5 P) 48:is a 1356:Olog 70:0–9 65:Top 36:is 1687:: 566:. 545:‎ 525:‎ 501:‎ 477:‎ 453:‎ 433:‎ 420:‎ 400:‎ 376:‎ 359:‎ 339:‎ 322:‎ 302:‎ 285:‎ 265:‎ 252:‎ 239:‎ 226:‎ 202:‎ 182:‎ 1655:W 1643:U 1616:T 1499:S 1482:R 1450:Q 1383:P 1351:O 1334:N 1297:M 1245:L 1208:K 1141:I 1109:H 1027:G 965:F 903:E 851:D 694:C 657:B 605:A 583:* 536:Σ 512:T 488:S 464:O 444:M 411:L 387:I 350:H 313:F 276:D 213:C 193:A 150:Z 147:Y 144:X 141:W 138:V 135:U 132:T 129:S 126:R 123:Q 120:P 117:O 114:N 111:M 108:L 105:K 102:J 99:I 96:H 93:G 90:F 87:E 84:D 81:C 78:B 75:A 42:.

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