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Talk:Distributive law between monads

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giving the ring monad (or the monoid and commutative monoid monads giving the semiring monad, which I guess works in exactly the same way) – at least one other algebraic example would be nice, but I'm not personally aware of one.
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The above is obviously not an appropriate way for a Knowledge article to begin. It doesn't tell the lay reader that mathematics (rather than chemistry, theology, video games, etc.) is what this is about.
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This article is in dire need of examples! Preferably more than just the prototypical example of the monoid and abelian group monads on
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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I have added an Examples section with a {needs expansion} tag for anyone who'd like to contribute :)
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https://web.archive.org/web/20110514231306/http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf
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for additional information. I made the following changes:
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http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf
313: 291: 218: 166: 329:, but I can't do that in the graphics embodying the 101:, a collaborative effort to improve the coverage of 394:using the archive tool instructions below. Editors 477: 321: 299: 256: 204: 380:This message was posted before February 2018. 8: 350:I have just modified one external link on 47: 19: 464: 462: 312: 290: 285:Also, I think it would be nice to change 245: 232: 217: 193: 180: 165: 317: 295: 49: 257:{\displaystyle (T,\mu ^{T},\eta ^{T})} 205:{\displaystyle (S,\mu ^{S},\eta ^{S})} 7: 95:This article is within the scope of 38:It is of interest to the following 14: 518:Low-priority mathematics articles 354:. Please take a moment to review 115:Knowledge:WikiProject Mathematics 471: 468: 465: 118:Template:WikiProject Mathematics 82: 72: 51: 20: 513:Stub-Class mathematics articles 352:Distributive law between monads 135:This article has been rated as 478:{\displaystyle \mathbf {Set} } 448:12:24, 11 September 2017 (UTC) 251: 219: 199: 167: 1: 499:00:54, 19 February 2024 (UTC) 338:00:29, 10 November 2006 (UTC) 109:and see a list of open tasks. 534: 411:(last update: 5 June 2024) 347:Hello fellow Wikipedians, 134: 67: 46: 141:project's priority scale 343:External links modified 322:{\displaystyle \ell \,} 98:WikiProject Mathematics 479: 323: 301: 258: 206: 28:This article is rated 480: 324: 302: 259: 207: 461: 392:regular verification 331:commutative diagrams 311: 289: 216: 164: 121:mathematics articles 382:After February 2018 300:{\displaystyle l\,} 475: 436:InternetArchiveBot 387:InternetArchiveBot 319: 318: 297: 296: 254: 202: 90:Mathematics portal 34:content assessment 412: 155: 154: 151: 150: 147: 146: 525: 484: 482: 481: 476: 474: 446: 437: 410: 409: 388: 328: 326: 325: 320: 306: 304: 303: 298: 263: 261: 260: 255: 250: 249: 237: 236: 211: 209: 208: 203: 198: 197: 185: 184: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 533: 532: 528: 527: 526: 524: 523: 522: 503: 502: 459: 458: 455: 440: 435: 403: 396:have permission 386: 360:this simple FaQ 345: 309: 308: 287: 286: 241: 228: 214: 213: 189: 176: 162: 161: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 531: 529: 521: 520: 515: 505: 504: 473: 470: 467: 454: 451: 430: 429: 422: 375: 374: 366:Added archive 344: 341: 316: 294: 279: 278: 277: 276: 253: 248: 244: 240: 235: 231: 227: 224: 221: 201: 196: 192: 188: 183: 179: 175: 172: 169: 153: 152: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 530: 519: 516: 514: 511: 510: 508: 501: 500: 496: 492: 487: 452: 450: 449: 444: 439: 438: 427: 423: 420: 416: 415: 414: 407: 401: 397: 393: 389: 383: 378: 373: 369: 365: 364: 363: 361: 357: 353: 348: 342: 340: 339: 336: 335:Michael Hardy 332: 314: 292: 283: 274: 271: 267: 246: 242: 238: 233: 229: 225: 222: 194: 190: 186: 181: 177: 173: 170: 160:Suppose that 159: 158: 157: 156: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 488: 456: 434: 431: 406:source check 385: 379: 376: 349: 346: 284: 280: 272: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 112:Mathematics 103:mathematics 59:Mathematics 507:Categories 443:Report bug 30:Stub-class 426:this tool 419:this tool 453:Examples 432:Cheers.— 270:category 264:are two 356:my edit 139:on the 491:Jayy V 266:monads 36:scale. 268:on a 495:talk 212:and 400:RfC 370:to 307:to 131:Low 509:: 497:) 413:. 408:}} 404:{{ 333:. 315:ℓ 243:η 230:μ 191:η 178:μ 493:( 472:t 469:e 466:S 445:) 441:( 428:. 421:. 293:l 275:. 273:C 252:) 247:T 239:, 234:T 226:, 223:T 220:( 200:) 195:S 187:, 182:S 174:, 171:S 168:( 143:. 42::

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Michael Hardy
00:29, 10 November 2006 (UTC)
Distributive law between monads
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https://web.archive.org/web/20110514231306/http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf
http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf
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