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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
114: 87: 561: 604: 293: 503: 549: 557: 490: 354:-module shares its name with the considerably better-known model for 178:
is equivalent to the category of finite sets and bijections.)
565: 410:. Note this functor then induces a group homomorphism 416: 338: 302: 276: 239: 217: 193: 158: 122: 90: 55: 27: 440: 346: 321: 284: 258: 225: 201: 166: 137: 105: 76: 35: 266:of finite-dimensional vector spaces over a field 585: 402:viewed as a category with a single object to 8: 472: 441:{\displaystyle G\to \operatorname {Aut} (X)} 71: 56: 592: 578: 489: 415: 358:due to Elmendorf, Kriz, Mandell and May. 340: 339: 337: 304: 303: 301: 278: 277: 275: 241: 240: 238: 219: 218: 216: 195: 194: 192: 160: 159: 157: 129: 125: 124: 121: 89: 54: 29: 28: 26: 152:is equivalent to the category of finite 465: 379: 314: 311: 308: 305: 251: 248: 245: 242: 450:Automorphism group#In category theory 7: 546: 544: 14: 548: 322:{\displaystyle {\mathsf {Vect}}} 259:{\displaystyle {\mathsf {Vect}}} 138:{\displaystyle \mathbb {S} _{n}} 406:that maps the single object to 368:Highly structured ring spectrum 435: 429: 420: 356:highly structured ring spectra 100: 94: 68: 62: 1: 504:"La renaissance des opĂ©rades" 564:. You can help Knowledge by 347:{\displaystyle \mathbb {S} } 285:{\displaystyle \mathbb {S} } 226:{\displaystyle \mathbb {S} } 202:{\displaystyle \mathbb {S} } 167:{\displaystyle \mathbb {S} } 113:comes with an action of the 36:{\displaystyle \mathbb {S} } 174:-sets (roughly because the 632: 543: 512:SĂ©minaire Nicolas Bourbaki 84:of objects such that each 473:Getzler & Jones 1994 233:-object in the category 77:{\displaystyle \{X(n)\}} 442: 348: 323: 286: 260: 227: 203: 168: 139: 107: 78: 37: 443: 386:An action of a group 349: 324: 292:-module determines a 287: 261: 228: 204: 169: 150:combinatorial species 140: 108: 79: 38: 414: 336: 300: 274: 237: 215: 191: 176:permutation category 156: 120: 106:{\displaystyle X(n)} 88: 53: 25: 332:This definition of 616:Algebraic topology 438: 398:is a functor from 344: 319: 282: 256: 223: 199: 164: 135: 103: 74: 47:symmetric sequence 33: 18:algebraic topology 573: 572: 500:Loday, Jean-Louis 623: 594: 587: 580: 558:topology-related 552: 545: 537: 535: 534: 495: 493: 476: 470: 453: 447: 445: 444: 439: 384: 353: 351: 350: 345: 343: 328: 326: 325: 320: 318: 317: 291: 289: 288: 283: 281: 265: 263: 262: 257: 255: 254: 232: 230: 229: 224: 222: 208: 206: 205: 200: 198: 173: 171: 170: 165: 163: 148:The category of 144: 142: 141: 136: 134: 133: 128: 112: 110: 109: 104: 83: 81: 80: 75: 49:) is a sequence 42: 40: 39: 34: 32: 631: 630: 626: 625: 624: 622: 621: 620: 601: 600: 599: 598: 541: 532: 530: 498: 483: 480: 479: 471: 467: 462: 457: 456: 412: 411: 385: 381: 376: 364: 334: 333: 298: 297: 272: 271: 235: 234: 213: 212: 189: 188: 184: 154: 153: 123: 118: 117: 115:symmetric group 86: 85: 51: 50: 45:(also called a 23: 22: 12: 11: 5: 629: 627: 619: 618: 613: 611:Topology stubs 603: 602: 597: 596: 589: 582: 574: 571: 570: 553: 539: 538: 508:www.numdam.org 496: 491:hep-th/9403055 478: 477: 464: 463: 461: 458: 455: 454: 437: 434: 431: 428: 425: 422: 419: 394:in a category 378: 377: 375: 372: 371: 370: 363: 360: 342: 316: 313: 310: 307: 280: 253: 250: 247: 244: 221: 197: 183: 180: 162: 132: 127: 102: 99: 96: 93: 73: 70: 67: 64: 61: 58: 31: 13: 10: 9: 6: 4: 3: 2: 628: 617: 614: 612: 609: 608: 606: 595: 590: 588: 583: 581: 576: 575: 569: 567: 563: 560:article is a 559: 554: 551: 547: 542: 529: 525: 521: 517: 513: 509: 505: 501: 497: 492: 487: 482: 481: 474: 469: 466: 459: 451: 432: 426: 423: 417: 409: 405: 401: 397: 393: 390:on an object 389: 383: 380: 373: 369: 366: 365: 361: 359: 357: 330: 295: 294:Schur functor 269: 211:, we mean an 210: 181: 179: 177: 151: 146: 130: 116: 97: 91: 65: 59: 48: 44: 19: 566:expanding it 555: 540: 531:. Retrieved 507: 468: 407: 403: 399: 395: 391: 387: 382: 331: 267: 187: 185: 147: 46: 21: 15: 605:Categories 533:2018-09-27 528:0866.18007 460:References 427:⁡ 421:→ 502:(1996). 362:See also 182:S-module 520:1423619 209:-module 43:-object 526:  518:  448:; cf. 556:This 486:arXiv 475:, § 1 374:Notes 20:, an 562:stub 524:Zbl 424:Aut 296:on 186:By 16:In 607:: 522:. 516:MR 514:. 510:. 506:. 329:. 145:. 593:e 586:t 579:v 568:. 536:. 494:. 488:: 452:. 436:) 433:X 430:( 418:G 408:X 404:C 400:G 396:C 392:X 388:G 341:S 315:t 312:c 309:e 306:V 279:S 268:k 252:t 249:c 246:e 243:V 220:S 196:S 161:S 131:n 126:S 101:) 98:n 95:( 92:X 72:} 69:) 66:n 63:( 60:X 57:{ 30:S

Index

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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