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Cyclic category

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22: 51: 531: 489: 465: 433: 73: 34: 355: 44: 38: 30: 222:+1 beads. More precisely, the morphisms can be identified with homotopy classes of degree 1 increasing maps from 55: 536: 107: 421: 411: 485: 461: 429: 453: 449: 338: 499: 374: 312:
A cyclic set is a contravariant functor from the cyclic category to sets. More generally a
495: 481: 370: 333: 103: 425: 525: 480:, Grundlehren der Mathematischen Wissenschaften , vol. 301, Berlin, New York: 396: 351: 460:, Encyclopaedia of Mathematical Sciences, vol. 38, Springer, pp. 60–61, 475: 87: 512: 400: 378: 416: 191:
represent the same morphism when their difference is divisible by
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can be thought of as maps of (oriented) necklaces with
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is a contravariant functor from the cyclic category to
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and degree-1 maps between them. It was introduced by
363:Comptes Rendus de l'Académie des Sciences, Série I 296:Λ of the cyclic category is a classifying space 43:but its sources remain unclear because it lacks 151:from the integers to the integers, such that 8: 415: 74:Learn how and when to remove this message 147:are represented by increasing functions 356:"Cohomologie cyclique et foncteurs Ext" 122:The cyclic category Λ has one object Λ 111: 7: 401:"Noncommutative Geometry Year 2000" 408:Highlights of mathematical physics 289:The cyclic category is self dual. 14: 226:to itself that map the subgroup 202:Informally, the morphisms from Λ 20: 458:Algebra V: Homological algebra 258:The number of morphisms from Λ 1: 532:Categories in category theory 553: 474:Loday, Jean-Louis (1992), 128:for each natural number 29:This article includes a 108:cyclically ordered sets 58:more precise citations. 406:, in Fokas, A. (ed.), 292:The classifying space 183:, where two functions 300:of the circle group 135:The morphisms from Λ 426:2000math.....11193C 410:, pp. 49–110, 454:Shafarevich, I. R. 100:category of cycles 31:list of references 491:978-3-540-53339-9 84: 83: 76: 544: 502: 470: 450:Kostrikin, A. I. 445: 444: 442: 419: 405: 392: 391: 389: 383: 377:, archived from 360: 339:Simplex category 79: 72: 68: 65: 59: 54:this article by 45:inline citations 24: 23: 16: 552: 551: 547: 546: 545: 543: 542: 541: 537:Homology theory 522: 521: 509: 492: 482:Springer-Verlag 477:Cyclic homology 473: 468: 448: 440: 438: 436: 403: 395: 387: 385: 384:on 4 March 2016 381: 369:(23): 953–958, 358: 350: 347: 334:Cyclic homology 330: 310: 269: 263: 256: 213: 207: 146: 140: 132:= 0, 1, 2, ... 127: 120: 92:cyclic category 80: 69: 63: 60: 49: 35:related reading 25: 21: 12: 11: 5: 550: 548: 540: 539: 534: 524: 523: 520: 519: 513:Cycle category 508: 507:External links 505: 504: 503: 490: 471: 466: 446: 434: 393: 346: 343: 342: 341: 336: 329: 326: 316:in a category 309: 306: 265: 259: 255: 252: 209: 203: 142: 136: 123: 119: 116: 96:cycle category 82: 81: 39:external links 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 549: 538: 535: 533: 530: 529: 527: 518: 514: 511: 510: 506: 501: 497: 493: 487: 483: 479: 478: 472: 469: 467:3-540-53373-7 463: 459: 455: 451: 447: 437: 435:0-8218-3223-9 431: 427: 423: 418: 413: 409: 402: 398: 397:Connes, Alain 394: 380: 376: 372: 368: 365:(in French), 364: 357: 353: 352:Connes, Alain 349: 348: 344: 340: 337: 335: 332: 331: 327: 325: 323: 319: 315: 314:cyclic object 307: 305: 303: 299: 295: 290: 287: 285: 281: 277: 273: 268: 262: 253: 251: 249: 245: 241: 237: 233: 229: 225: 221: 217: 212: 206: 200: 198: 194: 190: 186: 182: 178: 174: 170: 166: 162: 158: 154: 150: 145: 139: 133: 131: 126: 117: 115: 113: 112:Connes (1983) 109: 105: 101: 97: 93: 89: 78: 75: 67: 57: 53: 47: 46: 40: 36: 32: 27: 18: 17: 476: 457: 439:, retrieved 417:math/0011193 407: 386:, retrieved 379:the original 366: 362: 321: 317: 313: 311: 301: 297: 293: 291: 288: 283: 279: 275: 271: 266: 260: 257: 247: 243: 239: 235: 231: 227: 223: 219: 215: 210: 204: 201: 196: 192: 188: 184: 180: 176: 172: 168: 164: 160: 156: 152: 148: 143: 137: 134: 129: 124: 121: 99: 95: 91: 85: 70: 61: 50:Please help 42: 308:Cyclic sets 88:mathematics 56:introducing 526:Categories 345:References 254:Properties 118:Definition 106:of finite 64:June 2021 456:(1994), 399:(2002), 354:(1983), 328:See also 104:category 500:1217970 422:Bibcode 375:0777584 218:+1 and 52:improve 498:  488:  464:  441:15 May 432:  388:15 May 373:  90:, the 412:arXiv 404:(PDF) 382:(PDF) 359:(PDF) 278:+1)!/ 102:is a 37:, or 517:nLab 486:ISBN 462:ISBN 443:2011 430:ISBN 390:2011 270:is ( 264:to Λ 208:to Λ 187:and 167:) = 141:to Λ 515:in 367:296 286:!. 246:+1) 238:to 234:+1) 98:or 94:or 86:In 528:: 496:MR 494:, 484:, 452:; 428:, 420:, 371:MR 361:, 324:. 304:. 298:BS 250:. 242:/( 230:/( 199:. 175:)+ 114:. 41:, 33:, 424:: 414:: 322:C 318:C 302:S 294:B 284:n 282:! 280:m 276:n 274:+ 272:m 267:n 261:m 248:Z 244:n 240:Z 236:Z 232:m 228:Z 224:S 220:n 216:m 211:n 205:m 197:1 195:+ 193:n 189:g 185:f 181:1 179:+ 177:n 173:x 171:( 169:f 165:1 163:+ 161:m 159:+ 157:x 155:( 153:f 149:f 144:n 138:m 130:n 125:n 77:) 71:( 66:) 62:( 48:.

Index

list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
mathematics
category
cyclically ordered sets
Connes (1983)
Cyclic homology
Simplex category
Connes, Alain
"Cohomologie cyclique et foncteurs Ext"
MR
0777584
the original
Connes, Alain
"Noncommutative Geometry Year 2000"
arXiv
math/0011193
Bibcode
2000math.....11193C
ISBN
0-8218-3223-9
Kostrikin, A. I.
Shafarevich, I. R.
ISBN
3-540-53373-7

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