25:
1197:
130:
1109:
568:
723:
448:
2081:
2047:
2002:
1952:
1918:
1888:
1855:
1825:
1789:
1736:
1707:
1677:
1624:
1569:
1478:
1387:
1290:
1763:
1652:
1598:
1361:
1316:
1266:
850:
817:
787:
749:
654:
628:
590:
215:
1542:
393:
1510:
1454:
1422:
321:
289:
254:
422:
1339:
511:
491:
471:
361:
341:
190:
2142:
Jiri Adamek, Horst
Herrlich, George Strecker. Abstract and concrete categories: The joy of cats, Chapter 9, Injective Objects and Essential Embeddings,
54:
1043:
1126:
to this sequence and computing the homology of the resulting (not necessarily exact) sequence. This approach is used to define
526:
517:
1236:
2055:
76:
47:
2128:. Reprints in Theory and Applications of Categories, No. 17 (2006) pp. 1-507. orig. John Wiley. pp. 147–155.
2119:
Adamek, Jiri; Herrlich, Horst; Strecker, George (1990). "Sec. 9. Injective objects and essential embeddings".
684:
427:
974:
37:
2062:
2028:
1983:
1933:
1899:
1869:
1836:
1806:
1770:
1717:
1688:
1658:
1605:
1550:
1459:
1368:
1271:
2169:
170:
41:
33:
1746:
1635:
1581:
1344:
1299:
1249:
833:
800:
770:
732:
637:
611:
573:
198:
1515:
366:
982:
853:
193:
58:
1483:
1427:
1395:
294:
262:
227:
2013:
1185:
401:
1030:
931:
2143:
2120:
8:
935:
1324:
1293:
1147:
1143:
1009:
1001:
916:
496:
476:
456:
346:
326:
175:
129:
2094:
118:
2021:
1155:
1151:
947:
605:
102:
2051:
1115:
1017:
924:
756:
110:
94:
2144:
Republished in
Reprints and Applications of Categories, No. 17 (2006) pp. 1-507
1976:
1005:
959:
726:
657:
114:
2163:
912:
675:
2017:
1572:
1168:
1139:
222:
2006:
1131:
1127:
1013:
661:
521:
90:
1135:
986:
593:
106:
473:
in the above definition is not required to be uniquely determined by
1196:
993:
257:
608:, and this is still one of its primary areas of application. When
1575:, we are back to the injective objects that were treated above.
899:
1104:{\displaystyle 0\to X\to Q^{0}\to Q^{1}\to Q^{2}\to \cdots }
927:. Assuming the axiom of choice, the notions are equivalent.
1029:
If an abelian category has enough injectives, we can form
762:
563:{\displaystyle \operatorname {Hom} _{\mathbf {C} }(-,Q)}
2118:
2065:
2031:
1986:
1936:
1902:
1872:
1839:
1809:
1773:
1749:
1720:
1691:
1661:
1638:
1608:
1584:
1553:
1518:
1486:
1462:
1430:
1398:
1371:
1347:
1327:
1302:
1274:
1252:
1046:
895:. The injective hull is then uniquely determined by
836:
803:
773:
735:
687:
640:
614:
576:
529:
499:
479:
459:
430:
404:
369:
349:
329:
297:
265:
230:
201:
178:
604:The notion of injectivity was first formulated for
2075:
2041:
1996:
1979:, the injective objects with respect to the class
1963:
1946:
1912:
1882:
1849:
1819:
1783:
1757:
1730:
1701:
1671:
1646:
1618:
1592:
1563:
1536:
1504:
1472:
1448:
1416:
1381:
1355:
1333:
1310:
1284:
1260:
1103:
985:, and the injective hull of a metric space is its
844:
811:
781:
743:
717:
648:
622:
584:
562:
505:
485:
465:
442:
416:
387:
355:
335:
315:
283:
248:
209:
184:
2149:J. Rosicky, Injectivity and accessible categories
2122:Abstract and Concrete Categories: The Joy of Cats
2161:
46:but its sources remain unclear because it lacks
2156:-reflection and injective hulls of fibre spaces
520:category, it is equivalent to require that the
1150:. The categories being used are typically
2024:form the injective objects for the class
875:is an essential monomorphism with domain
77:Learn how and when to remove this message
1195:
599:
128:
923:, an injective object is necessarily a
2162:
137:is injective if, given a monomorphism
101:is a generalization of the concept of
16:Mathematical object in category theory
763:Enough injectives and injective hulls
718:{\displaystyle 0\to Q\to U\to V\to 0}
2114:
2112:
2110:
18:
819:, there exists a monomorphism from
424:factors through every monomorphism
13:
2068:
2058:of a partially ordered set is its
2034:
1989:
1939:
1905:
1875:
1842:
1812:
1776:
1723:
1694:
1664:
1611:
1556:
1465:
1374:
1277:
1037:we can form a long exact sequence
1004:, an injective object is always a
630:is an abelian category, an object
443:{\displaystyle X\hookrightarrow Y}
14:
2181:
2107:
1191:
1891:-essential morphism with domain
1751:
1640:
1586:
1349:
1304:
1254:
838:
805:
775:
737:
642:
616:
578:
536:
203:
23:
2152:F. Cagliari and S. Montovani, T
117:. The dual notion is that of a
105:. This concept is important in
2076:{\displaystyle {\mathcal {H}}}
2042:{\displaystyle {\mathcal {H}}}
1997:{\displaystyle {\mathcal {H}}}
1947:{\displaystyle {\mathcal {H}}}
1913:{\displaystyle {\mathcal {H}}}
1883:{\displaystyle {\mathcal {H}}}
1850:{\displaystyle {\mathcal {H}}}
1820:{\displaystyle {\mathcal {H}}}
1784:{\displaystyle {\mathcal {H}}}
1731:{\displaystyle {\mathcal {H}}}
1702:{\displaystyle {\mathcal {H}}}
1672:{\displaystyle {\mathcal {H}}}
1619:{\displaystyle {\mathcal {H}}}
1564:{\displaystyle {\mathcal {H}}}
1496:
1473:{\displaystyle {\mathcal {H}}}
1440:
1408:
1382:{\displaystyle {\mathcal {H}}}
1285:{\displaystyle {\mathcal {H}}}
1134:functors and also the various
1095:
1082:
1069:
1056:
1050:
709:
703:
697:
691:
557:
545:
434:
408:
307:
275:
240:
1:
2136:
2056:Dedekind–MacNeille completion
1012:, and therefore it is always
902:a non-canonical isomorphism.
124:
93:, especially in the field of
1758:{\displaystyle \mathbf {C} }
1647:{\displaystyle \mathbf {C} }
1593:{\displaystyle \mathbf {C} }
1356:{\displaystyle \mathbf {C} }
1311:{\displaystyle \mathbf {C} }
1261:{\displaystyle \mathbf {C} }
1114:and one can then define the
981:, an injective object is an
946:, an injective object is an
845:{\displaystyle \mathbf {C} }
812:{\displaystyle \mathbf {C} }
782:{\displaystyle \mathbf {C} }
744:{\displaystyle \mathbf {C} }
649:{\displaystyle \mathbf {C} }
623:{\displaystyle \mathbf {C} }
585:{\displaystyle \mathbf {C} }
210:{\displaystyle \mathbf {C} }
7:
2088:
905:
10:
2186:
2005:of anodyne extensions are
1537:{\displaystyle g\circ h=f}
1184:) or, more generally, any
1033:, i.e. for a given object
930:In the category of (left)
879:and an injective codomain
864:is a monomorphism only if
388:{\displaystyle h\circ f=g}
975:category of metric spaces
823:to an injective object.
570:carries monomorphisms in
2100:
1505:{\displaystyle g:B\to Q}
1480:there exists a morphism
1449:{\displaystyle h:A\to B}
1417:{\displaystyle f:A\to Q}
398:That is, every morphism
316:{\displaystyle h:Y\to Q}
291:there exists a morphism
284:{\displaystyle g:X\to Q}
249:{\displaystyle f:X\to Y}
32:This article includes a
1024:
970:has enough injectives).
755:is injective, then the
61:more precise citations.
2077:
2043:
2014:partially ordered sets
1998:
1948:
1914:
1884:
1851:
1821:
1785:
1759:
1732:
1703:
1673:
1648:
1620:
1594:
1565:
1538:
1506:
1474:
1450:
1418:
1392:if for every morphism
1383:
1357:
1335:
1312:
1286:
1268:be a category and let
1262:
1243:
1105:
983:injective metric space
854:essential monomorphism
846:
813:
791:have enough injectives
783:
745:
719:
650:
624:
586:
564:
507:
487:
467:
444:
418:
417:{\displaystyle X\to Q}
389:
357:
337:
317:
285:
250:
211:
186:
166:
2078:
2044:
1999:
1949:
1915:
1885:
1852:
1822:
1786:
1760:
1733:
1704:
1674:
1649:
1621:
1595:
1566:
1539:
1507:
1475:
1451:
1419:
1384:
1358:
1336:
1313:
1287:
1263:
1208:-injective if, given
1199:
1186:Grothendieck category
1106:
1031:injective resolutions
847:
814:
784:
746:
720:
651:
625:
600:In Abelian categories
587:
565:
508:
488:
468:
445:
419:
390:
358:
338:
318:
286:
251:
212:
187:
132:
113:and in the theory of
2063:
2029:
1984:
1934:
1921:-injective codomain
1900:
1870:
1837:
1807:
1794:if for any morphism
1771:
1747:
1718:
1689:
1659:
1636:
1628:if for every object
1606:
1582:
1551:
1516:
1484:
1460:
1428:
1396:
1369:
1345:
1325:
1300:
1272:
1250:
1044:
936:module homomorphisms
856:if for any morphism
834:
801:
793:if for every object
771:
733:
685:
638:
612:
574:
527:
497:
477:
457:
428:
402:
367:
347:
327:
295:
263:
228:
199:
176:
2012:In the category of
1975:In the category of
1710:-injective object.
1424:and every morphism
1118:of a given functor
1002:continuous mappings
992:In the category of
962:(as a consequence,
917:group homomorphisms
911:In the category of
868:is a monomorphism.
161:can be extended to
2073:
2039:
1994:
1970:-injective objects
1944:
1910:
1880:
1847:
1817:
1781:
1755:
1728:
1699:
1669:
1654:, there exists an
1644:
1616:
1590:
1561:
1534:
1502:
1470:
1446:
1414:
1379:
1353:
1331:
1308:
1282:
1258:
1244:
1152:functor categories
1148:algebraic geometry
1144:algebraic topology
1101:
1010:continuous lattice
842:
809:
779:
741:
715:
646:
620:
606:abelian categories
582:
560:
503:
483:
463:
440:
414:
385:
353:
333:
313:
281:
246:
207:
182:
167:
34:list of references
2095:Projective object
2022:complete lattices
1334:{\displaystyle Q}
1154:or categories of
506:{\displaystyle g}
486:{\displaystyle f}
466:{\displaystyle h}
363:, i.e. such that
356:{\displaystyle Y}
336:{\displaystyle g}
185:{\displaystyle Q}
119:projective object
97:, the concept of
87:
86:
79:
2177:
2130:
2129:
2127:
2116:
2084:-injective hull.
2082:
2080:
2079:
2074:
2072:
2071:
2052:order-embeddings
2048:
2046:
2045:
2040:
2038:
2037:
2003:
2001:
2000:
1995:
1993:
1992:
1969:
1968:
1953:
1951:
1950:
1945:
1943:
1942:
1919:
1917:
1916:
1911:
1909:
1908:
1889:
1887:
1886:
1881:
1879:
1878:
1856:
1854:
1853:
1848:
1846:
1845:
1826:
1824:
1823:
1818:
1816:
1815:
1798:, the composite
1790:
1788:
1787:
1782:
1780:
1779:
1764:
1762:
1761:
1756:
1754:
1737:
1735:
1734:
1729:
1727:
1726:
1708:
1706:
1705:
1700:
1698:
1697:
1678:
1676:
1675:
1670:
1668:
1667:
1653:
1651:
1650:
1645:
1643:
1625:
1623:
1622:
1617:
1615:
1614:
1599:
1597:
1596:
1591:
1589:
1571:is the class of
1570:
1568:
1567:
1562:
1560:
1559:
1543:
1541:
1540:
1535:
1511:
1509:
1508:
1503:
1479:
1477:
1476:
1471:
1469:
1468:
1455:
1453:
1452:
1447:
1423:
1421:
1420:
1415:
1388:
1386:
1385:
1380:
1378:
1377:
1362:
1360:
1359:
1354:
1352:
1340:
1338:
1337:
1332:
1317:
1315:
1314:
1309:
1307:
1296:of morphisms of
1291:
1289:
1288:
1283:
1281:
1280:
1267:
1265:
1264:
1259:
1257:
1116:derived functors
1110:
1108:
1107:
1102:
1094:
1093:
1081:
1080:
1068:
1067:
948:injective module
860:, the composite
851:
849:
848:
843:
841:
818:
816:
815:
810:
808:
788:
786:
785:
780:
778:
750:
748:
747:
742:
740:
724:
722:
721:
716:
655:
653:
652:
647:
645:
629:
627:
626:
621:
619:
591:
589:
588:
583:
581:
569:
567:
566:
561:
541:
540:
539:
512:
510:
509:
504:
492:
490:
489:
484:
472:
470:
469:
464:
449:
447:
446:
441:
423:
421:
420:
415:
394:
392:
391:
386:
362:
360:
359:
354:
342:
340:
339:
334:
322:
320:
319:
314:
290:
288:
287:
282:
255:
253:
252:
247:
216:
214:
213:
208:
206:
191:
189:
188:
183:
115:model categories
103:injective module
99:injective object
82:
75:
71:
68:
62:
57:this article by
48:inline citations
27:
26:
19:
2185:
2184:
2180:
2179:
2178:
2176:
2175:
2174:
2170:Category theory
2160:
2159:
2155:
2146:, Wiley (1990).
2139:
2134:
2133:
2125:
2117:
2108:
2103:
2091:
2067:
2066:
2064:
2061:
2060:
2033:
2032:
2030:
2027:
2026:
1988:
1987:
1985:
1982:
1981:
1977:simplicial sets
1972:
1966:
1965:
1954:-injective hull
1938:
1937:
1935:
1932:
1931:
1904:
1903:
1901:
1898:
1897:
1874:
1873:
1871:
1868:
1867:
1841:
1840:
1838:
1835:
1834:
1811:
1810:
1808:
1805:
1804:
1775:
1774:
1772:
1769:
1768:
1750:
1748:
1745:
1744:
1722:
1721:
1719:
1716:
1715:
1693:
1692:
1690:
1687:
1686:
1680:-morphism from
1663:
1662:
1660:
1657:
1656:
1639:
1637:
1634:
1633:
1610:
1609:
1607:
1604:
1603:
1585:
1583:
1580:
1579:
1555:
1554:
1552:
1549:
1548:
1517:
1514:
1513:
1485:
1482:
1481:
1464:
1463:
1461:
1458:
1457:
1429:
1426:
1425:
1397:
1394:
1393:
1373:
1372:
1370:
1367:
1366:
1348:
1346:
1343:
1342:
1326:
1323:
1322:
1303:
1301:
1298:
1297:
1276:
1275:
1273:
1270:
1269:
1253:
1251:
1248:
1247:
1241:
1237:factors through
1235:
1231:
1227:
1223:
1219:
1215:
1211:
1207:
1203:
1194:
1183:
1164:
1089:
1085:
1076:
1072:
1063:
1059:
1045:
1042:
1041:
1027:
1018:locally compact
997:
960:injective hulls
925:divisible group
908:
837:
835:
832:
831:
826:A monomorphism
804:
802:
799:
798:
774:
772:
769:
768:
765:
757:sequence splits
736:
734:
731:
730:
686:
683:
682:
669:
641:
639:
636:
635:
615:
613:
610:
609:
602:
577:
575:
572:
571:
535:
534:
530:
528:
525:
524:
498:
495:
494:
478:
475:
474:
458:
455:
454:
429:
426:
425:
403:
400:
399:
368:
365:
364:
348:
345:
344:
328:
325:
324:
296:
293:
292:
264:
261:
260:
229:
226:
225:
202:
200:
197:
196:
177:
174:
173:
164:
160:
156:
152:
148:
144:
140:
136:
127:
111:homotopy theory
95:category theory
83:
72:
66:
63:
52:
38:related reading
28:
24:
17:
12:
11:
5:
2183:
2173:
2172:
2158:
2157:
2153:
2150:
2147:
2138:
2135:
2132:
2131:
2105:
2104:
2102:
2099:
2098:
2097:
2090:
2087:
2086:
2085:
2070:
2036:
2010:
1991:
1971:
1962:
1941:
1907:
1877:
1844:
1814:
1778:
1753:
1725:
1696:
1666:
1642:
1613:
1588:
1558:
1533:
1530:
1527:
1524:
1521:
1501:
1498:
1495:
1492:
1489:
1467:
1445:
1442:
1439:
1436:
1433:
1413:
1410:
1407:
1404:
1401:
1376:
1363:is said to be
1351:
1330:
1306:
1279:
1256:
1239:
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1205:
1201:
1193:
1192:Generalization
1190:
1179:
1160:
1112:
1111:
1100:
1097:
1092:
1088:
1084:
1079:
1075:
1071:
1066:
1062:
1058:
1055:
1052:
1049:
1026:
1023:
1022:
1021:
1006:Scott topology
995:
990:
971:
928:
913:abelian groups
907:
904:
889:injective hull
840:
807:
777:
764:
761:
739:
727:exact sequence
714:
711:
708:
705:
702:
699:
696:
693:
690:
665:
658:if and only if
644:
618:
601:
598:
580:
559:
556:
553:
550:
547:
544:
538:
533:
502:
482:
462:
439:
436:
433:
413:
410:
407:
384:
381:
378:
375:
372:
352:
332:
312:
309:
306:
303:
300:
280:
277:
274:
271:
268:
245:
242:
239:
236:
233:
217:is said to be
205:
181:
162:
158:
154:
150:
146:
142:
138:
134:
126:
123:
85:
84:
42:external links
31:
29:
22:
15:
9:
6:
4:
3:
2:
2182:
2171:
2168:
2167:
2165:
2151:
2148:
2145:
2141:
2140:
2124:
2123:
2115:
2113:
2111:
2106:
2096:
2093:
2092:
2083:
2057:
2053:
2049:
2023:
2019:
2018:monotone maps
2015:
2011:
2008:
2007:Kan complexes
2004:
1978:
1974:
1973:
1961:
1959:
1955:
1929:is called an
1928:
1924:
1920:
1894:
1890:
1864:
1859:
1857:
1831:
1827:
1801:
1797:
1793:
1791:
1742:
1738:
1711:
1709:
1683:
1679:
1631:
1627:
1578:The category
1576:
1574:
1573:monomorphisms
1545:
1531:
1528:
1525:
1522:
1519:
1499:
1493:
1490:
1487:
1443:
1437:
1434:
1431:
1411:
1405:
1402:
1399:
1391:
1389:
1328:
1319:
1295:
1238:
1198:
1189:
1187:
1182:
1178:
1174:
1170:
1166:
1163:
1159:
1153:
1149:
1145:
1141:
1137:
1133:
1129:
1125:
1121:
1117:
1098:
1090:
1086:
1077:
1073:
1064:
1060:
1053:
1047:
1040:
1039:
1038:
1036:
1032:
1019:
1015:
1011:
1007:
1003:
999:
991:
988:
984:
980:
976:
972:
969:
965:
961:
957:
953:
949:
945:
941:
937:
933:
929:
926:
922:
918:
914:
910:
909:
903:
901:
898:
894:
890:
887:is called an
886:
882:
878:
874:
869:
867:
863:
859:
855:
852:is called an
829:
824:
822:
796:
792:
767:The category
760:
758:
754:
728:
712:
706:
700:
694:
688:
679:
677:
673:
668:
663:
659:
656:is injective
633:
607:
597:
595:
554:
551:
548:
542:
531:
523:
519:
518:locally small
514:
500:
480:
460:
453:The morphism
451:
437:
431:
411:
405:
396:
382:
379:
376:
373:
370:
350:
330:
310:
304:
301:
298:
278:
272:
269:
266:
259:
243:
237:
234:
231:
224:
221:if for every
220:
195:
179:
172:
131:
122:
120:
116:
112:
108:
104:
100:
96:
92:
81:
78:
70:
60:
56:
50:
49:
43:
39:
35:
30:
21:
20:
2121:
2059:
2025:
1980:
1964:Examples of
1957:
1930:
1926:
1922:
1896:
1892:
1866:
1862:
1860:
1833:
1829:
1803:
1799:
1795:
1767:
1766:
1740:
1714:
1712:
1685:
1681:
1655:
1629:
1602:have enough
1601:
1577:
1546:
1365:
1364:
1320:
1245:
1180:
1176:
1172:
1169:ringed space
1161:
1157:
1140:group theory
1138:theories in
1123:
1122:by applying
1119:
1113:
1034:
1028:
978:
967:
963:
955:
951:
943:
939:
920:
896:
892:
888:
884:
880:
876:
872:
870:
865:
861:
857:
827:
825:
820:
794:
790:
766:
752:
680:
671:
666:
631:
603:
515:
452:
397:
223:monomorphism
218:
168:
98:
88:
73:
67:October 2021
64:
53:Please help
45:
1626:-injectives
1600:is said to
1156:sheaves of
789:is said to
662:hom functor
522:hom functor
91:mathematics
59:introducing
2137:References
2054:, and the
1792:-essential
1765:is called
1739:-morphism
1390:-injective
1321:An object
1200:An object
1167:over some
1136:cohomology
987:tight span
751:such that
596:set maps.
594:surjective
323:extending
256:and every
133:An object
125:Definition
107:cohomology
1523:∘
1497:→
1441:→
1409:→
1099:⋯
1096:→
1083:→
1070:→
1057:→
1051:→
710:→
704:→
698:→
692:→
670:(–,
549:−
543:
435:↪
409:→
374:∘
308:→
276:→
241:→
219:injective
2164:Category
2089:See also
1828:only if
1228: :
1212: :
906:Examples
258:morphism
194:category
153: :
141: :
1925:, then
1895:and an
1165:modules
973:In the
932:modules
883:, then
55:improve
2020:, the
1832:is in
1802:is in
1684:to an
1224:, any
1130:, and
998:spaces
725:is an
171:object
149:, any
2126:(PDF)
2101:Notes
1865:is a
1512:with
1294:class
1292:be a
1014:sober
1008:on a
900:up to
676:exact
674:) is
516:In a
192:in a
109:, in
40:, or
2016:and
1246:Let
1146:and
1025:Uses
1016:and
1000:and
958:has
934:and
915:and
660:its
493:and
2050:of
1960:.
1956:of
1861:If
1743:in
1632:of
1547:If
1456:in
1341:of
1220:in
1204:is
1132:Tor
1128:Ext
979:Met
968:Mod
956:Mod
944:Mod
891:of
871:If
830:in
797:of
729:in
681:If
664:Hom
634:of
592:to
532:Hom
343:to
169:An
89:In
2166::
2109:^
1858:.
1800:fg
1713:A
1544:.
1318:.
1232:→
1216:→
1188:.
1175:,
1142:,
977:,
950:.
938:,
921:Ab
919:,
862:fg
759:.
678:.
513:.
450:.
395:.
157:→
145:→
121:.
44:,
36:,
2154:0
2069:H
2035:H
2009:.
1990:H
1967:H
1958:X
1940:H
1927:G
1923:G
1906:H
1893:X
1876:H
1863:g
1843:H
1830:f
1813:H
1796:f
1777:H
1752:C
1741:g
1724:H
1695:H
1682:X
1665:H
1641:C
1630:X
1612:H
1587:C
1557:H
1532:f
1529:=
1526:h
1520:g
1500:Q
1494:B
1491::
1488:g
1466:H
1444:B
1438:A
1435::
1432:h
1412:Q
1406:A
1403::
1400:f
1375:H
1350:C
1329:Q
1305:C
1278:H
1255:C
1242:.
1240:h
1234:Q
1230:A
1226:f
1222:H
1218:B
1214:A
1210:h
1206:H
1202:Q
1181:X
1177:O
1173:X
1171:(
1162:X
1158:O
1124:F
1120:F
1091:2
1087:Q
1078:1
1074:Q
1065:0
1061:Q
1054:X
1048:0
1035:X
1020:.
996:0
994:T
989:.
966:-
964:R
954:-
952:R
942:-
940:R
897:X
893:X
885:G
881:G
877:X
873:g
866:f
858:f
839:C
828:g
821:X
806:C
795:X
776:C
753:Q
738:C
713:0
707:V
701:U
695:Q
689:0
672:Q
667:C
643:C
632:Q
617:C
579:C
558:)
555:Q
552:,
546:(
537:C
501:g
481:f
461:h
438:Y
432:X
412:Q
406:X
383:g
380:=
377:f
371:h
351:Y
331:g
311:Q
305:Y
302::
299:h
279:Q
273:X
270::
267:g
244:Y
238:X
235::
232:f
204:C
180:Q
165:.
163:Y
159:Q
155:X
151:g
147:Y
143:X
139:f
135:Q
80:)
74:(
69:)
65:(
51:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
