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Simplicial group

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What is a simplicial commutative ring from the point of view of homotopy theory?
383: 329: 70: 426: 315:. Progress in Mathematics. Vol. 174. Basel, Boston, Berlin: Birkhäuser. 106: 278: 262: 379: 94: 281:(1945), "Harmonische Funktionen und Randwertaufgaben in einem Komplex", 296: 357: 371: 105:
says that a simplicial abelian group may be identified with a
109:. In fact it can be shown that any simplicial abelian group 349: 143: 115: 217:discusses a simplicial analogue of the fact that a 207:in the category of simplicial abelian groups is a 193: 121: 69:In mathematics, more precisely, in the theory of 424: 194:{\displaystyle \prod _{i\geq 0}K(\pi _{i}A,i).} 407: 310: 266: 414: 400: 277: 214: 14: 425: 334:An introduction to homological algebra 311:Goerss, P. G.; Jardine, J. F. (1999). 366: 29: 24: 25: 449: 339: 284:Commentarii Mathematici Helvetici 370: 34: 27:Mathematical concept in topology 269:, Ch 3. Proposition 2.20) 255: 185: 163: 89:is a simplicial object in the 13: 1: 248: 386:. You can help Knowledge by 261:Paul Goerss and 7: 243:Simplicial commutative ring 236: 209:simplicial commutative ring 46:Simplicial commutative ring 43:It has been suggested that 10: 454: 365: 313:Simplicial Homotopy Theory 93:. A simplicial group is a 91:category of abelian groups 233:from these observations. 60:Proposed since July 2024. 231:Kirchhoff's circuit laws 135:Eilenberg–MacLane spaces 87:simplicial abelian group 18:Simplicial abelian group 227:harmonic representative 103:Dold–Kan correspondence 382:-related article is a 195: 123: 196: 124: 141: 113: 97:(in particular, its 53:into this article. ( 131:homotopy equivalent 129:is non-canonically 297:10.1007/BF02566245 205:commutative monoid 191: 159: 119: 83:category of groups 438:Mathematics stubs 395: 394: 322:978-3-7643-6064-1 144: 122:{\displaystyle A} 101:make sense). The 79:simplicial object 67: 66: 62: 16:(Redirected from 445: 416: 409: 402: 374: 367: 346:simplicial group 326: 307: 270: 259: 219:cohomology class 200: 198: 197: 192: 175: 174: 158: 133:to a product of 128: 126: 125: 120: 75:simplicial group 58: 38: 37: 30: 21: 453: 452: 448: 447: 446: 444: 443: 442: 433:Simplicial sets 423: 422: 421: 420: 363: 342: 323: 274: 273: 260: 256: 251: 239: 223:Kähler manifold 170: 166: 148: 142: 139: 138: 114: 111: 110: 99:homotopy groups 85:. Similarly, a 71:simplicial sets 63: 39: 35: 28: 23: 22: 15: 12: 11: 5: 451: 441: 440: 435: 419: 418: 411: 404: 396: 393: 392: 375: 361: 360: 355: 341: 340:External links 338: 337: 336: 330:Charles Weibel 327: 321: 308: 272: 271: 253: 252: 250: 247: 246: 245: 238: 235: 215:Eckmann (1945) 190: 187: 184: 181: 178: 173: 169: 165: 162: 157: 154: 151: 147: 118: 65: 64: 42: 40: 33: 26: 9: 6: 4: 3: 2: 450: 439: 436: 434: 431: 430: 428: 417: 412: 410: 405: 403: 398: 397: 391: 389: 385: 381: 376: 373: 369: 368: 364: 359: 356: 354: 352: 347: 344: 343: 335: 331: 328: 324: 318: 314: 309: 306: 302: 298: 294: 290: 286: 285: 280: 279:Eckmann, Beno 276: 275: 268: 264: 258: 254: 244: 241: 240: 234: 232: 228: 225:has a unique 224: 220: 216: 212: 210: 206: 201: 188: 182: 179: 176: 171: 167: 160: 155: 152: 149: 145: 136: 132: 116: 108: 107:chain complex 104: 100: 96: 92: 88: 84: 80: 76: 72: 61: 56: 52: 48: 47: 41: 32: 31: 19: 388:expanding it 377: 362: 350: 333: 312: 288: 282: 263:Rick Jardine 257: 229:and deduces 213: 202: 86: 74: 68: 59: 44: 380:mathematics 291:: 240–255, 95:Kan complex 427:Categories 249:References 168:π 153:≥ 146:∏ 237:See also 348:at the 305:0013318 265: ( 81:in the 55:Discuss 319:  303:  51:merged 378:This 221:on a 77:is a 384:stub 317:ISBN 267:1999 73:, a 353:Lab 293:doi 49:be 429:: 332:, 301:MR 299:, 289:17 287:, 211:. 203:A 137:, 415:e 408:t 401:v 390:. 351:n 325:. 295:: 189:. 186:) 183:i 180:, 177:A 172:i 164:( 161:K 156:0 150:i 117:A 57:) 20:)

Index

Simplicial abelian group
Simplicial commutative ring
merged
Discuss
simplicial sets
simplicial object
category of groups
category of abelian groups
Kan complex
homotopy groups
Dold–Kan correspondence
chain complex
homotopy equivalent
Eilenberg–MacLane spaces
commutative monoid
simplicial commutative ring
Eckmann (1945)
cohomology class
Kähler manifold
harmonic representative
Kirchhoff's circuit laws
Simplicial commutative ring
Rick Jardine
1999
Eckmann, Beno
Commentarii Mathematici Helvetici
doi
10.1007/BF02566245
MR
0013318

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