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Simplicial group

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What is a simplicial commutative ring from the point of view of homotopy theory?
83: 304:. Progress in Mathematics. Vol. 174. Basel, Boston, Berlin: Birkhäuser. 360: 270:(1945), "Harmonische Funktionen und Randwertaufgaben in einem Komplex", 285: 346: 338: 94:
says that a simplicial abelian group may be identified with a
18: 98:. In fact it can be shown that any simplicial abelian group 376: 132: 104: 206:discusses a simplicial analogue of the fact that a 196:in the category of simplicial abelian groups is a 182: 110: 58:In mathematics, more precisely, in the theory of 183:{\displaystyle \prod _{i\geq 0}K(\pi _{i}A,i).} 396: 255: 8: 403: 389: 159: 137: 131: 103: 243: 203: 323:An introduction to homological algebra 300:Goerss, P. G.; Jardine, J. F. (1999). 7: 357: 355: 14: 273:Commentarii Mathematici Helvetici 359: 23: 16:Mathematical concept in topology 258:, Ch 3. Proposition 2.20) 174: 152: 78:is a simplicial object in the 1: 375:. You can help Knowledge by 250:Paul Goerss and 232:Simplicial commutative ring 198:simplicial commutative ring 35:Simplicial commutative ring 32:It has been suggested that 443: 354: 302:Simplicial Homotopy Theory 82:. A simplicial group is a 80:category of abelian groups 222:from these observations. 49:Proposed since July 2024. 220:Kirchhoff's circuit laws 124:Eilenberg–MacLane spaces 76:simplicial abelian group 216:harmonic representative 92:Dold–Kan correspondence 371:-related article is a 184: 112: 185: 113: 130: 102: 86:(in particular, its 42:into this article. ( 120:homotopy equivalent 118:is non-canonically 286:10.1007/BF02566245 194:commutative monoid 180: 148: 108: 72:category of groups 427:Mathematics stubs 384: 383: 311:978-3-7643-6064-1 133: 111:{\displaystyle A} 90:make sense). The 68:simplicial object 56: 55: 51: 434: 405: 398: 391: 363: 356: 335:simplicial group 315: 296: 259: 248: 208:cohomology class 189: 187: 186: 181: 164: 163: 147: 122:to a product of 117: 115: 114: 109: 64:simplicial group 47: 27: 26: 19: 442: 441: 437: 436: 435: 433: 432: 431: 422:Simplicial sets 412: 411: 410: 409: 352: 331: 312: 299: 266: 263: 262: 249: 245: 240: 228: 212:Kähler manifold 155: 128: 127: 100: 99: 88:homotopy groups 74:. Similarly, a 60:simplicial sets 52: 28: 24: 17: 12: 11: 5: 440: 438: 430: 429: 424: 414: 413: 408: 407: 400: 393: 385: 382: 381: 364: 350: 349: 344: 330: 329:External links 327: 326: 325: 319:Charles Weibel 316: 310: 297: 261: 260: 242: 241: 239: 236: 235: 234: 227: 224: 204:Eckmann (1945) 179: 176: 173: 170: 167: 162: 158: 154: 151: 146: 143: 140: 136: 107: 54: 53: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 439: 428: 425: 423: 420: 419: 417: 406: 401: 399: 394: 392: 387: 386: 380: 378: 374: 370: 365: 362: 358: 353: 348: 345: 343: 341: 336: 333: 332: 328: 324: 320: 317: 313: 307: 303: 298: 295: 291: 287: 283: 279: 275: 274: 269: 268:Eckmann, Beno 265: 264: 257: 253: 247: 244: 237: 233: 230: 229: 225: 223: 221: 217: 214:has a unique 213: 209: 205: 201: 199: 195: 190: 177: 171: 168: 165: 160: 156: 149: 144: 141: 138: 134: 125: 121: 105: 97: 96:chain complex 93: 89: 85: 81: 77: 73: 69: 65: 61: 50: 45: 41: 37: 36: 30: 21: 20: 377:expanding it 366: 351: 339: 322: 301: 277: 271: 252:Rick Jardine 246: 218:and deduces 202: 191: 75: 63: 57: 48: 33: 369:mathematics 280:: 240–255, 84:Kan complex 416:Categories 238:References 157:π 142:≥ 135:∏ 226:See also 337:at the 294:0013318 254: ( 70:in the 44:Discuss 308:  292:  40:merged 367:This 210:on a 66:is a 373:stub 306:ISBN 256:1999 62:, a 342:Lab 282:doi 38:be 418:: 321:, 290:MR 288:, 278:17 276:, 200:. 192:A 126:, 404:e 397:t 390:v 379:. 340:n 314:. 284:: 178:. 175:) 172:i 169:, 166:A 161:i 153:( 150:K 145:0 139:i 106:A 46:)

Index

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
ISBN

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