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Getzler, Ezra; Jones, J. D. S. (1994-03-08). "Operads, homotopy algebra and iterated integrals for double loop spaces".
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of characteristic zero (the symmetric groups act from the right by convention). Then each
125: 98: 572: 615: 304: 514: 17: 560: 568: 501: 365:-module shares its name with the considerably better-known model for 189:
is equivalent to the category of finite sets and bijections.)
576: 421:. Note this functor then induces a group homomorphism 427: 349: 313: 287: 250: 228: 204: 169: 133: 101: 66: 38: 451: 357: 332: 295: 269: 236: 212: 177: 148: 116: 87: 46: 277:of finite-dimensional vector spaces over a field 596: 413:viewed as a category with a single object to 8: 483: 452:{\displaystyle G\to \operatorname {Aut} (X)} 82: 67: 603: 589: 500: 426: 369:due to Elmendorf, Kriz, Mandell and May. 351: 350: 348: 315: 314: 312: 289: 288: 286: 252: 251: 249: 230: 229: 227: 206: 205: 203: 171: 170: 168: 140: 136: 135: 132: 100: 65: 40: 39: 37: 163:is equivalent to the category of finite 476: 390: 325: 322: 319: 316: 262: 259: 256: 253: 461:Automorphism group#In category theory 7: 557: 555: 25: 559: 333:{\displaystyle {\mathsf {Vect}}} 270:{\displaystyle {\mathsf {Vect}}} 149:{\displaystyle \mathbb {S} _{n}} 417:that maps the single object to 379:Highly structured ring spectrum 446: 440: 431: 367:highly structured ring spectra 111: 105: 79: 73: 1: 515:"La renaissance des opĂ©rades" 575:. You can help Knowledge by 358:{\displaystyle \mathbb {S} } 296:{\displaystyle \mathbb {S} } 237:{\displaystyle \mathbb {S} } 213:{\displaystyle \mathbb {S} } 178:{\displaystyle \mathbb {S} } 124:comes with an action of the 47:{\displaystyle \mathbb {S} } 185:-sets (roughly because the 643: 554: 523:SĂ©minaire Nicolas Bourbaki 95:of objects such that each 484:Getzler & Jones 1994 244:-object in the category 88:{\displaystyle \{X(n)\}} 453: 359: 334: 297: 271: 238: 214: 179: 150: 118: 89: 48: 454: 397:An action of a group 360: 335: 303:-module determines a 298: 272: 239: 215: 180: 161:combinatorial species 151: 119: 90: 49: 425: 347: 311: 285: 248: 226: 202: 187:permutation category 167: 131: 117:{\displaystyle X(n)} 99: 64: 36: 343:This definition of 627:Algebraic topology 449: 409:is a functor from 355: 330: 293: 267: 234: 210: 175: 146: 114: 85: 58:symmetric sequence 44: 29:algebraic topology 18:Symmetric sequence 584: 583: 511:Loday, Jean-Louis 16:(Redirected from 634: 605: 598: 591: 569:topology-related 563: 556: 548: 546: 545: 506: 504: 487: 481: 464: 458: 456: 455: 450: 395: 364: 362: 361: 356: 354: 339: 337: 336: 331: 329: 328: 302: 300: 299: 294: 292: 276: 274: 273: 268: 266: 265: 243: 241: 240: 235: 233: 219: 217: 216: 211: 209: 184: 182: 181: 176: 174: 159:The category of 155: 153: 152: 147: 145: 144: 139: 123: 121: 120: 115: 94: 92: 91: 86: 60:) is a sequence 53: 51: 50: 45: 43: 21: 642: 641: 637: 636: 635: 633: 632: 631: 612: 611: 610: 609: 552: 543: 541: 509: 494: 491: 490: 482: 478: 473: 468: 467: 423: 422: 396: 392: 387: 375: 345: 344: 309: 308: 283: 282: 246: 245: 224: 223: 200: 199: 195: 165: 164: 134: 129: 128: 126:symmetric group 97: 96: 62: 61: 56:(also called a 34: 33: 23: 22: 15: 12: 11: 5: 640: 638: 630: 629: 624: 622:Topology stubs 614: 613: 608: 607: 600: 593: 585: 582: 581: 564: 550: 549: 519:www.numdam.org 507: 502:hep-th/9403055 489: 488: 475: 474: 472: 469: 466: 465: 448: 445: 442: 439: 436: 433: 430: 405:in a category 389: 388: 386: 383: 382: 381: 374: 371: 353: 327: 324: 321: 318: 291: 264: 261: 258: 255: 232: 208: 194: 191: 173: 143: 138: 113: 110: 107: 104: 84: 81: 78: 75: 72: 69: 42: 24: 14: 13: 10: 9: 6: 4: 3: 2: 639: 628: 625: 623: 620: 619: 617: 606: 601: 599: 594: 592: 587: 586: 580: 578: 574: 571:article is a 570: 565: 562: 558: 553: 540: 536: 532: 528: 524: 520: 516: 512: 508: 503: 498: 493: 492: 485: 480: 477: 470: 462: 443: 437: 434: 428: 420: 416: 412: 408: 404: 401:on an object 400: 394: 391: 384: 380: 377: 376: 372: 370: 368: 341: 306: 305:Schur functor 280: 222:, we mean an 221: 192: 190: 188: 162: 157: 141: 127: 108: 102: 76: 70: 59: 55: 30: 19: 577:expanding it 566: 551: 542:. Retrieved 518: 479: 418: 414: 410: 406: 402: 398: 393: 342: 278: 198: 196: 158: 57: 32: 26: 616:Categories 544:2018-09-27 539:0866.18007 471:References 438:⁡ 432:→ 513:(1996). 373:See also 193:S-module 531:1423619 220:-module 54:-object 537:  529:  459:; cf. 567:This 497:arXiv 486:, § 1 385:Notes 31:, an 573:stub 535:Zbl 435:Aut 307:on 197:By 27:In 618:: 533:. 527:MR 525:. 521:. 517:. 340:. 156:. 604:e 597:t 590:v 579:. 547:. 505:. 499:: 463:. 447:) 444:X 441:( 429:G 419:X 415:C 411:G 407:C 403:X 399:G 352:S 326:t 323:c 320:e 317:V 290:S 279:k 263:t 260:c 257:e 254:V 231:S 207:S 172:S 142:n 137:S 112:) 109:n 106:( 103:X 83:} 80:) 77:n 74:( 71:X 68:{ 41:S 20:)

Index

Symmetric sequence
algebraic topology
symmetric group
combinatorial species
permutation category
Schur functor
highly structured ring spectra
Highly structured ring spectrum
Automorphism group#In category theory
Getzler & Jones 1994
arXiv
hep-th/9403055
Loday, Jean-Louis
"La renaissance des opérades"
SĂ©minaire Nicolas Bourbaki
MR
1423619
Zbl
0866.18007
Stub icon
topology-related
stub
expanding it
v
t
e
Categories
Topology stubs
Algebraic topology

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