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Operad algebra

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be symmetric monoidal ∞-category with monoidal structure distributive over colimits. If
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Hinich, Vladimir (1997-02-11). "Homological algebra of homotopy algebras".
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is a homotopy equivalence, then the ∞-category of algebras over
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is symmetric monoidal, this recovers the usual definition.
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http://ncatlab.org/nlab/show/algebra+over+an+operad
100:, then one can say an algebra over an operad is an 251: 148: 168:is equivalent to the ∞-category of algebras over 351: 8: 81:for short, is, roughly, a left module over 358: 344: 274: 243: 237: 236: 233: 124: 202: 156:is a map of operads and, moreover, if 85:with multiplications parametrized by 7: 312: 310: 209: 252:{\displaystyle {\mathcal {E}}_{n}} 25: 228:"Derived Algebraic Geometry Over 314: 35:. It is a generalization of an 135: 1: 65:symmetric monoidal ∞-category 330:. You can help Knowledge by 43:, with an operad replacing 398: 309: 149:{\displaystyle f:O\to O'} 39:over a commutative ring 31:is an "algebra" over an 382:Abstract algebra stubs 326:-related article is a 253: 150: 72:algebra over an operad 18:Algebra over an operad 254: 151: 232: 191:Homotopy Lie algebra 123: 37:associative algebra 249: 212:, Proposition 2.9. 146: 104:-monoid object in 98:topological operad 61:symmetric sequence 339: 338: 16:(Redirected from 389: 377:Abstract algebra 360: 353: 346: 324:abstract algebra 318: 311: 298: 280: 278: 265: 263: 258: 256: 255: 250: 248: 247: 242: 241: 213: 207: 155: 153: 152: 147: 145: 55:Given an operad 21: 397: 396: 392: 391: 390: 388: 387: 386: 367: 366: 365: 364: 307: 290: 287: 268: 261: 235: 230: 229: 226:Francis, John. 225: 222: 217: 216: 208: 204: 199: 182: 138: 121: 120: 53: 27:In algebra, an 23: 22: 15: 12: 11: 5: 395: 393: 385: 384: 379: 369: 368: 363: 362: 355: 348: 340: 337: 336: 319: 305: 304: 299: 286: 285:External links 283: 282: 281: 266: 246: 240: 221: 218: 215: 214: 201: 200: 198: 195: 194: 193: 188: 181: 178: 144: 141: 137: 134: 131: 128: 52: 49: 29:operad algebra 24: 14: 13: 10: 9: 6: 4: 3: 2: 394: 383: 380: 378: 375: 374: 372: 361: 356: 354: 349: 347: 342: 341: 335: 333: 329: 325: 320: 317: 313: 308: 303: 300: 297: 293: 289: 288: 284: 277: 276:q-alg/9702015 272: 267: 260: 244: 224: 223: 219: 211: 206: 203: 196: 192: 189: 187: 184: 183: 179: 177: 175: 171: 167: 163: 159: 142: 139: 132: 129: 126: 118: 113: 111: 107: 103: 99: 95: 90: 88: 84: 80: 78: 73: 69: 66: 62: 58: 50: 48: 46: 42: 38: 34: 30: 19: 332:expanding it 321: 306: 295: 205: 173: 169: 165: 161: 157: 116: 114: 109: 105: 101: 93: 91: 86: 82: 76: 75: 71: 67: 56: 54: 44: 40: 28: 26: 296:ncatlab.org 51:Definitions 371:Categories 220:References 136:→ 292:"operad" 180:See also 143:′ 79:-algebra 59:(say, a 259:-Rings" 210:Francis 186:En-ring 70:), an 33:operad 322:This 271:arXiv 262:(PDF) 197:Notes 108:. If 96:is a 74:, or 63:in a 328:stub 115:Let 172:in 164:in 92:If 373:: 294:, 176:. 170:O' 89:. 47:. 359:e 352:t 345:v 334:. 279:. 273:: 264:. 245:n 239:E 174:C 166:C 162:O 158:f 140:O 133:O 130:: 127:f 117:C 110:C 106:C 102:O 94:O 87:O 83:O 77:O 68:C 57:O 45:R 41:R 20:)

Index

Algebra over an operad
operad
associative algebra
symmetric sequence
symmetric monoidal ∞-category
topological operad
En-ring
Homotopy Lie algebra
Francis
"Derived Algebraic Geometry Over E n {\displaystyle {\mathcal {E}}_{n}} -Rings"
arXiv
q-alg/9702015
"operad"
http://ncatlab.org/nlab/show/algebra+over+an+operad
Stub icon
abstract algebra
stub
expanding it
v
t
e
Categories
Abstract algebra
Abstract algebra stubs

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