Applications of categorical algebra;: [proceedings

Title Page......Page 1
Preface......Page 3
Contents......Page 5
0.......Page 7
1.......Page 11
2.......Page 18
1. Introduction......Page 21
2. Simplicial category......Page 22
3. Homology......Page 24
4. Comparison theorem......Page 25
5. Spectral sequence......Page 29
6. Generalization......Page 31
7. Simplicial resolutions......Page 34
8. Construction of simplicial resolutions (Part I)......Page 35
9. Attaching cells......Page 36
10. Construction of simplicial resolutions (Part II)......Page 39
References......Page 42
On completing bicartesian squares......Page 43
Bibliography......Page 55
1. The axioms......Page 56
2. Abelian objects......Page 63
3. Structures and Modules......Page 66
4. Singular extensions; the Baer theory......Page 68
Reference......Page 70
On the (co-) homology of commutative rings......Page 71
1. Derived functors......Page 72
2. Homology and cohomology for universal algebras......Page 74
3. Associative algebra cohomology......Page 76
4. Cohomology of commutative rings, the relative cotangent complex......Page 77
5. The transitivity, flat base change, and vanishing theorems......Page 79
6. The fundamental spectral sequence......Page 82
7. Degeneracy of the fundamental spectral sequence in characteristic zero......Page 85
8. Relations with associative algebra cohomology......Page 86
9. Differential graded algebra resolutions in characteristic zero......Page 88
10. Local noetherian rings......Page 90
11. Euler characteristics for graded rings......Page 92
Bibliography......Page 93
Nonabelian homological algebra and K-theory......Page 94
1. Simplicial sets and complexes......Page 95
2. Simplicial homotopies......Page 99
3. Simplicial cofibrations......Page 101
4. Simplicial resolutions......Page 107
5. Aspherical models......Page 110
6. Group valued functors......Page 114
7. Topological K-theory......Page 117
8. Algebraic K-theory......Page 118
9. Excision and Mayer-Vietoris sequence......Page 125
Bibliography......Page 128
1. A graph-theoretic result......Page 130
2. The bipolar structure......Page 131
3. Pregroups......Page 132
4. The characterization of infinitely-ended groups......Page 133
References......Page 134
Hopf fibration towers and the unstable Adams spectral sequence......Page 135
1. Some categories and constructions......Page 137
2. The tower and spectral sequence......Page 141
3. Elementary properties of the functor <-1>: H⁎H/k → H⁎H/k......Page 143
4. Elementary properties of the tower......Page 147
5. Some functors of unstable A*-modules......Page 150
6. The algebra H*......Page 156
7. E²(X): A special case......Page 158
Appendix......Page 161
Bibliography......Page 165
1. Cancellation......Page 167
2. Spherical retracts......Page 170
3. Primary spaces......Page 172
4. The localized categories......Page 175
5. Uniqueness theorems......Page 177
6. The Grothendieck ring......Page 178
7. The basic theorem of local stable homotopy......Page 179
8. The infinite localization......Page 184
9. Injective envelopes in F......Page 185
10. Injective envelopes in F_p......Page 187
Bibliography......Page 189
1. Wilder's theorem......Page 190
2. The Wall invariant......Page 192
3. Properties of the Wall invariant......Page 194
4. Fibration......Page 196
References......Page 197
1. Notation and recollection of some facts from algebraic K-theory......Page 198
2. The category C(R,α) and the group C(R,α)......Page 202
3. The formula for K₁R_α[T]......Page 208
4. Applications......Page 217
References......Page 224
1.......Page 225
2. The proofs......Page 227
3. Examples......Page 229
References......Page 230
Author index......Page 233
Subject index......Page 235