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Isomorphism-closed subcategory

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33: 286: 528: 313: 482: 458: 434: 399: 221: 189: 162: 375: 256: 54: 333: 105: 77: 84: 124: 91: 488: 58: 73: 43: 62: 47: 559: 98: 165: 261: 543: 502: 496: 291: 463: 439: 415: 380: 202: 170: 143: 338: 229: 405: 318: 553: 492: 17: 224: 138: 32: 539: 499:. Every topological property corresponds to a strictly full subcategory of 538:
This article incorporates material from Isomorphism-closed subcategory on
412:. In the case of full subcategories it is sufficient to check that every 26: 469: 445: 421: 386: 297: 273: 208: 176: 149: 491:
one usually studies properties that are invariant under
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This condition is very natural. For example, in the
522: 476: 452: 428: 393: 369: 327: 307: 280: 250: 215: 183: 156: 544:Creative Commons Attribution/Share-Alike License 137:In category theory, a branch of mathematics, a 404:A subcategory that is isomorphism closed and 8: 61:. Unsourced material may be challenged and 506: 504: 468: 467: 465: 444: 443: 441: 420: 419: 417: 385: 384: 382: 346: 340: 320: 296: 295: 293: 272: 271: 263: 231: 207: 206: 204: 175: 174: 172: 148: 147: 145: 125:Learn how and when to remove this message 7: 59:adding citations to reliable sources 281:{\displaystyle A\in {\mathcal {A}}} 25: 436:-object that is isomorphic to an 513: 510: 507: 74:"Isomorphism-closed subcategory" 31: 523:{\displaystyle \mathbf {Top} .} 308:{\displaystyle {\mathcal {A}}.} 542:, which is licensed under the 489:category of topological spaces 477:{\displaystyle {\mathcal {A}}} 453:{\displaystyle {\mathcal {A}}} 429:{\displaystyle {\mathcal {B}}} 394:{\displaystyle {\mathcal {A}}} 361: 242: 216:{\displaystyle {\mathcal {B}}} 184:{\displaystyle {\mathcal {B}}} 157:{\displaystyle {\mathcal {A}}} 1: 370:{\displaystyle h^{-1}:B\to A} 576: 251:{\displaystyle h:A\to B} 315:This implies that both 524: 497:topological properties 478: 454: 430: 395: 371: 329: 309: 282: 252: 217: 185: 158: 525: 479: 455: 431: 396: 372: 330: 310: 283: 253: 218: 186: 159: 503: 464: 440: 416: 381: 339: 319: 292: 262: 230: 203: 171: 144: 55:improve this article 460:-object is also an 520: 474: 450: 426: 391: 367: 325: 305: 278: 248: 213: 193:isomorphism closed 181: 154: 18:Isomorphism-closed 328:{\displaystyle B} 135: 134: 127: 109: 16:(Redirected from 567: 529: 527: 526: 521: 516: 483: 481: 480: 475: 473: 472: 459: 457: 456: 451: 449: 448: 435: 433: 432: 427: 425: 424: 400: 398: 397: 392: 390: 389: 376: 374: 373: 368: 354: 353: 334: 332: 331: 326: 314: 312: 311: 306: 301: 300: 287: 285: 284: 279: 277: 276: 257: 255: 254: 249: 222: 220: 219: 214: 212: 211: 190: 188: 187: 182: 180: 179: 163: 161: 160: 155: 153: 152: 130: 123: 119: 116: 110: 108: 67: 35: 27: 21: 575: 574: 570: 569: 568: 566: 565: 564: 560:Category theory 550: 549: 535: 501: 500: 462: 461: 438: 437: 414: 413: 379: 378: 342: 337: 336: 317: 316: 290: 289: 260: 259: 228: 227: 201: 200: 169: 168: 142: 141: 131: 120: 114: 111: 68: 66: 52: 36: 23: 22: 15: 12: 11: 5: 573: 571: 563: 562: 552: 551: 534: 531: 519: 515: 512: 509: 493:homeomorphisms 471: 447: 423: 388: 366: 363: 360: 357: 352: 349: 345: 324: 304: 299: 275: 270: 267: 247: 244: 241: 238: 235: 210: 191:is said to be 178: 151: 133: 132: 115:September 2024 39: 37: 30: 24: 14: 13: 10: 9: 6: 4: 3: 2: 572: 561: 558: 557: 555: 548: 547: 545: 541: 532: 530: 517: 498: 494: 490: 485: 411: 410:strictly full 407: 402: 364: 358: 355: 350: 347: 343: 322: 302: 268: 265: 245: 239: 236: 233: 226: 198: 194: 167: 140: 129: 126: 118: 107: 104: 100: 97: 93: 90: 86: 83: 79: 76: –  75: 71: 70:Find sources: 64: 60: 56: 50: 49: 45: 40:This article 38: 34: 29: 28: 19: 537: 536: 486: 409: 403: 196: 192: 136: 121: 112: 102: 95: 88: 81: 69: 53:Please help 41: 495:—so-called 288:belongs to 225:isomorphism 139:subcategory 540:PlanetMath 533:References 408:is called 401:as well. 377:belong to 85:newspapers 484:-object. 362:→ 348:− 269:∈ 243:→ 199:if every 42:does not 554:Category 166:category 197:replete 99:scholar 63:removed 48:sources 101:  94:  87:  80:  72:  258:with 164:of a 106:JSTOR 92:books 406:full 335:and 78:news 46:any 44:cite 195:or 57:by 556:: 546:. 518:. 514:p 511:o 508:T 470:A 446:A 422:B 387:A 365:A 359:B 356:: 351:1 344:h 323:B 303:. 298:A 274:A 266:A 246:B 240:A 237:: 234:h 223:- 209:B 177:B 150:A 128:) 122:( 117:) 113:( 103:· 96:· 89:· 82:· 65:. 51:. 20:)

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Isomorphism-closed

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subcategory
category
isomorphism
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category of topological spaces
homeomorphisms
topological properties
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Category theory

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