Knowledge (XXG)

Fibrant object

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in the category. This property makes fibrant objects the "correct" objects on which to define
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Dually is the notion of cofibrant object, defined to be an object
219: 156: 130: 110: 162: 142: 116: 239: 8: 246: 232: 155: 129: 109: 131: 7: 200: 198: 89:, the fibrant objects are known as 85:. In the context of the theory of 218:. You can help Knowledge (XXG) by 14: 143:{\displaystyle \varnothing \to c} 202: 179:P.G. Goerss and J.F. Jardine, 134: 124:such that the unique morphism 73:are characterized by having a 1: 275:Differential geometry stubs 150:from the initial object to 291: 197: 181:Simplicial Homotopy Theory 270:Objects (category theory) 69:The fibrant objects of a 214:-related article is a 164: 144: 118: 75:right lifting property 212:differential geometry 165: 145: 119: 71:closed model category 154: 128: 108: 77:with respect to any 27:in the context of a 16:Mathematical concept 79:trivial cofibration 170:is a cofibration. 160: 140: 114: 23:, specifically in 227: 226: 163:{\displaystyle c} 117:{\displaystyle c} 282: 248: 241: 234: 206: 199: 169: 167: 166: 161: 149: 147: 146: 141: 123: 121: 120: 115: 290: 289: 285: 284: 283: 281: 280: 279: 265:Homotopy theory 255: 254: 253: 252: 195: 176: 152: 151: 126: 125: 106: 105: 97:. They are the 87:simplicial sets 83:homotopy groups 67: 55:terminal object 25:homotopy theory 17: 12: 11: 5: 288: 286: 278: 277: 272: 267: 257: 256: 251: 250: 243: 236: 228: 225: 224: 207: 193: 192: 175: 172: 159: 139: 136: 133: 113: 101:over a point. 99:Kan fibrations 66: 63: 36:fibrant object 29:model category 15: 13: 10: 9: 6: 4: 3: 2: 287: 276: 273: 271: 268: 266: 263: 262: 260: 249: 244: 242: 237: 235: 230: 229: 223: 221: 217: 213: 208: 205: 201: 196: 190: 189:3-7643-6064-X 186: 182: 178: 177: 173: 171: 157: 137: 111: 102: 100: 96: 92: 91:Kan complexes 88: 84: 80: 76: 72: 64: 62: 60: 56: 52: 48: 44: 40: 37: 33: 30: 26: 22: 220:expanding it 209: 194: 180: 103: 90: 68: 42: 38: 35: 31: 18: 49:that has a 21:mathematics 259:Categories 174:References 95:Daniel Kan 65:Properties 135:→ 132:∅ 51:fibration 59:category 57:of the 53:to the 187:  93:after 47:object 45:is an 210:This 216:stub 185:ISBN 34:, a 41:of 19:In 261:: 61:. 247:e 240:t 233:v 222:. 191:. 158:c 138:c 112:c 43:M 39:A 32:M

Index

mathematics
homotopy theory
model category
object
fibration
terminal object
category
closed model category
right lifting property
trivial cofibration
homotopy groups
simplicial sets
Daniel Kan
Kan fibrations
ISBN
3-7643-6064-X
Stub icon
differential geometry
stub
expanding it
v
t
e
Categories
Homotopy theory
Objects (category theory)
Differential geometry stubs

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