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Conservative functor

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is conservative. In contrast, the forgetful functor from
400: 206:
Homological Algebra: In Strongly Non-Abelian Settings
37: 55: 420: 272: 8: 427: 413: 279: 265: 257: 114:, are conservative. More generally, every 36: 154: 126:is not conservative because not every 7: 381: 379: 14: 383: 47: 1: 399:. You can help Knowledge by 467: 378: 173:Courier Dover Publications 168:Category Theory in Context 295: 56:{\displaystyle F:C\to D} 203:Grandis, Marco (2013). 395:-related article is a 330:Essentially surjective 57: 451:Category theory stubs 58: 245:Conservative functor 128:continuous bijection 35: 26:conservative functor 90:is an isomorphism. 100:forgetful functors 63:such that for any 53: 408: 407: 373: 372: 345:Full and faithful 145:is conservative. 143:balanced category 458: 429: 422: 415: 387: 380: 281: 274: 267: 258: 232: 231: 229: 227: 211:World Scientific 200: 194: 193: 191: 189: 159: 139:faithful functor 62: 60: 59: 54: 466: 465: 461: 460: 459: 457: 456: 455: 446:Category theory 436: 435: 434: 433: 393:category theory 376: 374: 369: 291: 285: 241: 236: 235: 225: 223: 221: 202: 201: 197: 187: 185: 183: 161: 160: 156: 151: 116:monadic functor 106:, such as from 96: 33: 32: 18:category theory 12: 11: 5: 464: 462: 454: 453: 448: 438: 437: 432: 431: 424: 417: 409: 406: 405: 388: 371: 370: 368: 367: 362: 357: 352: 347: 342: 337: 332: 327: 322: 317: 312: 307: 302: 296: 293: 292: 286: 284: 283: 276: 269: 261: 255: 254: 240: 239:External links 237: 234: 233: 219: 195: 181: 153: 152: 150: 147: 95: 92: 52: 49: 46: 43: 40: 20:, a branch of 13: 10: 9: 6: 4: 3: 2: 463: 452: 449: 447: 444: 443: 441: 430: 425: 423: 418: 416: 411: 410: 404: 402: 398: 394: 389: 386: 382: 377: 366: 363: 361: 360:Representable 358: 356: 353: 351: 348: 346: 343: 341: 338: 336: 333: 331: 328: 326: 323: 321: 318: 316: 313: 311: 308: 306: 303: 301: 298: 297: 294: 289: 282: 277: 275: 270: 268: 263: 262: 259: 253: 251: 246: 243: 242: 238: 222: 216: 212: 208: 207: 199: 196: 184: 178: 174: 170: 169: 164: 158: 155: 148: 146: 144: 140: 135: 133: 132:homeomorphism 129: 125: 121: 117: 113: 109: 105: 101: 93: 91: 89: 86:implies that 85: 81: 77: 73: 69: 66: 50: 44: 41: 38: 31: 27: 23: 19: 401:expanding it 390: 375: 310:Conservative 309: 249: 224:. Retrieved 205: 198: 186:. Retrieved 167: 163:Riehl, Emily 157: 136: 123: 119: 111: 107: 97: 87: 79: 75: 71: 67: 25: 15: 188:18 February 84:isomorphism 82:) being an 22:mathematics 440:Categories 226:14 January 220:9814425931 182:048680903X 149:References 340:Forgetful 48:→ 355:Monoidal 325:Enriched 320:Diagonal 300:Additive 165:(2016). 94:Examples 65:morphism 350:Logical 315:Derived 305:Adjoint 288:Functor 247:at the 141:from a 104:algebra 30:functor 365:Smooth 217:  179:  137:Every 391:This 335:Exact 290:types 130:is a 28:is a 397:stub 228:2017 215:ISBN 190:2017 177:ISBN 98:The 24:, a 252:Lab 124:Set 122:to 120:Top 112:Set 110:to 108:Grp 102:in 70:in 16:In 442:: 213:. 209:. 175:. 171:. 134:. 74:, 428:e 421:t 414:v 403:. 280:e 273:t 266:v 250:n 230:. 192:. 88:f 80:f 78:( 76:F 72:C 68:f 51:D 45:C 42:: 39:F

Index

category theory
mathematics
functor
morphism
isomorphism
forgetful functors
algebra
monadic functor
continuous bijection
homeomorphism
faithful functor
balanced category
Riehl, Emily
Category Theory in Context
Courier Dover Publications
ISBN
048680903X
Homological Algebra: In Strongly Non-Abelian Settings
World Scientific
ISBN
9814425931
Conservative functor
nLab
v
t
e
Functor
Additive
Adjoint
Conservative

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