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621: 120: 405: 292: 554: 476: 366: 249: 194: 60: 444: 331: 508: 662: 214: 593: 655: 696: 686: 648: 681: 691: 74: 161: 371: 258: 513: 449: 339: 222: 167: 33: 126: 410: 297: 142: 138: 134: 481: 589: 632: 130: 17: 603: 599: 565: 149: 628: 199: 66: 675: 25: 620: 217: 570: 157: 588:. Pure and applied mathematics. Vol. 17. Academic Press. 636: 516: 484: 452: 413: 374: 342: 300: 261: 225: 202: 170: 77: 36: 548: 502: 470: 438: 399: 360: 325: 286: 243: 208: 188: 114: 54: 656: 8: 663: 649: 534: 521: 515: 483: 451: 424: 412: 379: 373: 341: 311: 299: 266: 260: 224: 201: 169: 92: 78: 76: 35: 115:{\displaystyle {\text{coim}}f=A/\ker(f)} 7: 617: 615: 400:{\displaystyle f_{z}:Z\rightarrow Y} 287:{\displaystyle f_{c}:C\rightarrow Y} 635:. You can help Knowledge (XXG) by 549:{\displaystyle f_{z}=f_{c}\circ h} 14: 619: 471:{\displaystyle h:Z\rightarrow C} 361:{\displaystyle z:X\rightarrow Z} 244:{\displaystyle c:X\rightarrow C} 189:{\displaystyle f:X\rightarrow Y} 55:{\displaystyle f:A\rightarrow B} 462: 439:{\displaystyle f=f_{z}\circ z} 391: 352: 326:{\displaystyle f=f_{c}\circ c} 278: 235: 180: 109: 103: 46: 1: 145:, when that theorem applies. 713: 614: 503:{\displaystyle c=h\circ z} 160:is the dual notion of the 368:for which there is a map 143:first isomorphism theorem 584:Mitchell, Barry (1965). 446:, there is a unique map 631:-related article is a 550: 504: 472: 440: 401: 362: 327: 288: 245: 210: 190: 135:canonically isomorphic 116: 56: 551: 505: 473: 441: 402: 363: 328: 289: 246: 216:(if it exists) is an 211: 191: 117: 57: 697:Linear algebra stubs 687:Isomorphism theorems 586:Theory of categories 514: 482: 450: 411: 372: 340: 336:for any epimorphism 298: 259: 223: 200: 196:, then a coimage of 168: 75: 34: 162:image of a morphism 148:More generally, in 546: 500: 468: 436: 397: 358: 323: 284: 241: 206: 186: 133:. The coimage is 112: 52: 644: 643: 595:978-0-124-99250-4 209:{\displaystyle f} 81: 704: 682:Abstract algebra 665: 658: 651: 623: 616: 607: 555: 553: 552: 547: 539: 538: 526: 525: 509: 507: 506: 501: 477: 475: 474: 469: 445: 443: 442: 437: 429: 428: 406: 404: 403: 398: 384: 383: 367: 365: 364: 359: 332: 330: 329: 324: 316: 315: 293: 291: 290: 285: 271: 270: 250: 248: 247: 242: 215: 213: 212: 207: 195: 193: 192: 187: 121: 119: 118: 113: 96: 82: 79: 61: 59: 58: 53: 712: 711: 707: 706: 705: 703: 702: 701: 692:Category theory 672: 671: 670: 669: 612: 610: 596: 583: 579: 566:Quotient object 562: 530: 517: 512: 511: 480: 479: 478:such that both 448: 447: 420: 409: 408: 375: 370: 369: 338: 337: 307: 296: 295: 262: 257: 256: 255:there is a map 221: 220: 198: 197: 166: 165: 150:category theory 73: 72: 32: 31: 12: 11: 5: 710: 708: 700: 699: 694: 689: 684: 674: 673: 668: 667: 660: 653: 645: 642: 641: 629:linear algebra 624: 609: 608: 594: 580: 578: 575: 574: 573: 568: 561: 558: 557: 556: 545: 542: 537: 533: 529: 524: 520: 499: 496: 493: 490: 487: 467: 464: 461: 458: 455: 435: 432: 427: 423: 419: 416: 396: 393: 390: 387: 382: 378: 357: 354: 351: 348: 345: 334: 322: 319: 314: 310: 306: 303: 283: 280: 277: 274: 269: 265: 240: 237: 234: 231: 228: 205: 185: 182: 179: 176: 173: 123: 122: 111: 108: 105: 102: 99: 95: 91: 88: 85: 63: 62: 51: 48: 45: 42: 39: 13: 10: 9: 6: 4: 3: 2: 709: 698: 695: 693: 690: 688: 685: 683: 680: 679: 677: 666: 661: 659: 654: 652: 647: 646: 640: 638: 634: 630: 625: 622: 618: 613: 605: 601: 597: 591: 587: 582: 581: 576: 572: 569: 567: 564: 563: 559: 543: 540: 535: 531: 527: 522: 518: 497: 494: 491: 488: 485: 465: 459: 456: 453: 433: 430: 425: 421: 417: 414: 394: 388: 385: 380: 376: 355: 349: 346: 343: 335: 320: 317: 312: 308: 304: 301: 281: 275: 272: 267: 263: 254: 253: 252: 238: 232: 229: 226: 219: 203: 183: 177: 174: 171: 163: 159: 155: 151: 146: 144: 140: 136: 132: 128: 106: 100: 97: 93: 89: 86: 83: 71: 70: 69: 68: 49: 43: 40: 37: 30: 29: 28: 27: 23: 19: 637:expanding it 626: 611: 585: 153: 147: 124: 64: 26:homomorphism 21: 15: 218:epimorphism 676:Categories 577:References 251:such that 541:∘ 495:∘ 463:→ 431:∘ 392:→ 353:→ 318:∘ 279:→ 236:→ 181:→ 101:⁡ 47:→ 571:Cokernel 560:See also 158:morphism 67:quotient 604:0202787 154:coimage 141:by the 137:to the 129:by the 125:of the 65:is the 22:coimage 18:algebra 602:  592:  164:. If 152:, the 131:kernel 127:domain 20:, the 627:This 407:with 294:with 156:of a 139:image 24:of a 633:stub 590:ISBN 510:and 80:coim 98:ker 16:In 678:: 600:MR 598:. 664:e 657:t 650:v 639:. 606:. 544:h 536:c 532:f 528:= 523:z 519:f 498:z 492:h 489:= 486:c 466:C 460:Z 457:: 454:h 434:z 426:z 422:f 418:= 415:f 395:Y 389:Z 386:: 381:z 377:f 356:Z 350:X 347:: 344:z 333:, 321:c 313:c 309:f 305:= 302:f 282:Y 276:C 273:: 268:c 264:f 239:C 233:X 230:: 227:c 204:f 184:Y 178:X 175:: 172:f 110:) 107:f 104:( 94:/ 90:A 87:= 84:f 50:B 44:A 41:: 38:f

Index

algebra
homomorphism
quotient
domain
kernel
canonically isomorphic
image
first isomorphism theorem
category theory
morphism
image of a morphism
epimorphism
Quotient object
Cokernel
ISBN
978-0-124-99250-4
MR
0202787
Stub icon
linear algebra
stub
expanding it
v
t
e
Categories
Abstract algebra
Isomorphism theorems
Category theory
Linear algebra stubs

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