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Lawvere theory

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159: 75: 120: 371: 467: 78: 115: 111: 391: 325: 53: 386: 216: 92: 35: 411: 419: 8: 423: 372:"The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads" 442: 447: 39: 437: 427: 396: 315: 385:(Computation, Meaning, and Logic: Articles dedicated to Gordon Plotkin): 437–458, 407: 320: 31: 17: 400: 344: 100: 461: 367: 107: 28: 25: 451: 432: 88: 38:
that can be considered a categorical counterpart of the notion of an
418:, vol. 50, no. 5, Columbia University, pp. 869–872, 274:
Lawvere theories together with maps between them form the category
83: 247:′) is a finite-product preserving functor that commutes with 172:
with finite products is a finite-product preserving functor
348: 255:′. Such a map is commonly seen as an interpretation of ( 154:{\displaystyle I:\aleph _{0}^{\text{op}}\rightarrow L} 123: 56: 153: 69: 459: 379:Electronic Notes in Theoretical Computer Science 222: 412:"Functorial Semantics of Algebraic Theories" 366: 441: 431: 390: 406: 460: 13: 168:of a Lawvere theory in a category 131: 58: 14: 479: 114:and a strict identity-on-objects 338: 145: 1: 360: 281: 45: 223:Category of Lawvere theories 161:preserving finite products. 7: 401:10.1016/j.entcs.2007.02.019 309: 70:{\displaystyle \aleph _{0}} 10: 484: 231:between Lawvere theories ( 300:infinitary Lawvere theory 331: 326:Monad (category theory) 370:; Power, John (2007), 217:natural transformation 155: 71: 433:10.1073/pnas.50.5.869 304:finite-product theory 156: 72: 121: 54: 424:1963PNAS...50..869L 408:Lawvere, William F. 286:Variations include 144: 188:morphism of models 151: 130: 67: 468:Categorical logic 142: 40:equational theory 475: 454: 445: 435: 403: 394: 376: 354: 342: 316:Algebraic theory 202: 185: 160: 158: 157: 152: 143: 140: 138: 81:of the category 76: 74: 73: 68: 66: 65: 483: 482: 478: 477: 476: 474: 473: 472: 458: 457: 392:10.1.1.158.5440 374: 363: 358: 357: 343: 339: 334: 321:Clone (algebra) 312: 284: 225: 190: 173: 139: 134: 122: 119: 118: 106:with (strictly 61: 57: 55: 52: 51: 48: 32:William Lawvere 18:category theory 12: 11: 5: 481: 471: 470: 456: 455: 404: 368:Hyland, Martin 362: 359: 356: 355: 345:Lawvere theory 336: 335: 333: 330: 329: 328: 323: 318: 311: 308: 296:Lawvere theory 283: 280: 224: 221: 211:are models of 150: 147: 137: 133: 129: 126: 101:small category 99:consists of a 97:Lawvere theory 95:. Formally, a 64: 60: 47: 44: 22:Lawvere theory 9: 6: 4: 3: 2: 480: 469: 466: 465: 463: 453: 449: 444: 439: 434: 429: 425: 421: 417: 413: 409: 405: 402: 398: 393: 388: 384: 380: 373: 369: 365: 364: 353: 351: 346: 341: 337: 327: 324: 322: 319: 317: 314: 313: 307: 305: 301: 297: 293: 289: 279: 277: 272: 270: 266: 262: 258: 254: 250: 246: 242: 238: 234: 230: 220: 219:of functors. 218: 214: 210: 206: 201: 197: 193: 189: 184: 180: 176: 171: 167: 162: 148: 135: 127: 124: 117: 113: 109: 105: 102: 98: 94: 90: 86: 85: 80: 62: 43: 41: 37: 33: 30: 29:mathematician 27: 24:(named after 23: 19: 415: 382: 378: 349: 340: 303: 299: 295: 291: 287: 285: 275: 273: 268: 264: 260: 256: 252: 248: 244: 240: 236: 232: 228: 226: 212: 208: 204: 199: 195: 191: 187: 182: 178: 174: 169: 165: 163: 103: 96: 82: 49: 21: 15: 288:multisorted 108:associative 89:finite sets 416:PhD Thesis 361:References 292:multityped 282:Variations 46:Definition 387:CiteSeerX 146:→ 132:ℵ 110:) finite 93:functions 59:ℵ 462:Category 452:16591125 410:(1963), 310:See also 267:′,  243:′,  194: : 177: : 112:products 79:skeleton 36:category 26:American 420:Bibcode 347:at the 259:,  239:) and ( 235:,  116:functor 34:) is a 450:  443:221940 440:  389:  302:, and 263:) in ( 203:where 84:FinSet 375:(PDF) 332:Notes 215:is a 186:. A 166:model 77:be a 448:PMID 290:(or 271:′). 251:and 207:and 91:and 50:Let 20:, a 438:PMC 428:doi 397:doi 383:172 352:Lab 276:Law 229:map 87:of 16:In 464:: 446:, 436:, 426:, 414:, 395:, 381:, 377:, 306:. 298:, 294:) 278:. 227:A 198:→ 181:→ 164:A 141:op 42:. 430:: 422:: 399:: 350:n 269:I 265:L 261:I 257:L 253:I 249:I 245:I 241:L 237:I 233:L 213:L 209:N 205:M 200:N 196:M 192:h 183:C 179:L 175:M 170:C 149:L 136:0 128:: 125:I 104:L 63:0

Index

category theory
American
mathematician
William Lawvere
category
equational theory
skeleton
FinSet
finite sets
functions
small category
associative
products
functor
natural transformation
Algebraic theory
Clone (algebra)
Monad (category theory)
Lawvere theory
nLab
Hyland, Martin
"The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads"
CiteSeerX
10.1.1.158.5440
doi
10.1016/j.entcs.2007.02.019
Lawvere, William F.
"Functorial Semantics of Algebraic Theories"
Bibcode
1963PNAS...50..869L

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