 -homology groups 314
 -(co)homology group 331 352
-local module or spectrum 407
 -tower 390
 category 7
duality 13
 --sequence 471
-equivalence 110
-localization 110 471
-primary spectrum 116
-primary torsion spectrum 114
 -periodic module 224 327 413
-semi-triangulated 217 454
 -periodic spectrum 291 413
-semi-trianguIated category 286 454
-spectrum 82
(-) localization of an abelian group 471
(-)completion 132 254
(-)local abelian group 472
(-)torsion spectrum 114 125
(Graded) exterior algebra 172
(Graded) polynomial algebra 172
(Graded) symmetric algebra 172
(H-)acyclic spectrum 101
(H-)local spectrum 101
(H-)localization 101 295 430
(r-)skeleton 39 93
(Reduced) cohomology theory 5
(Reduced) homology theory 5
2-stage tower functor 297
A-completion 134
Adams category of CW-spectra 27
Adams filtration 274
Adams spectral sequence 274
Adams tower 273
Additive functor 440
Adjoint functor 65 440
Algebra (graded) 170
Bockstein operations 87
Bott periodic spectra 292
Bounded below 24 170
Brown — Peterson spectrum 83 434
C-theory 90
Calculus of left fractions 105 450
Cardinality continuous 105
Category of fractions 101 450
Category over R 111 443
Cellular tower 39 92
Central subalgebra 172
class 439
Cocommutative coproduct 185 356
Coexact sequence 4
Cofinal functor 445
Coherent diagram 443
Coherent module 170 194
Cohomology functor 46
Cohomotopy functor 46 264 292
Coinitial functor 445
Cokernel 445
Colimit 151 219 287 443
Collection 439
Commutative algebra 172
Completed cellular tower 152 290
Cone functor 3
Conjugation (canonical antiautomorphism) 186
Connected module 170
Connected ring spectrum 356
Coproduct 20 444
Coproduct (of Hopf algebra) 185
Coproduct category 443
Corepresentable functor 440
Crude cellular tower 39
Cylinder functor 3
Degree 442
Deloopable 222 401
Desuspendable 287 401 433
Diagram over an indexing category 443
Doubling functor 248
Dual module 179
Dual spectrum 66
Dual tower 8
Eilenberg — MacLane spectra 82 86
Equivalent category 441
Essential map 172
Eventually periodic spectrum 292
Exact functor 10 440 455
Exact triangle 8 20 453
Exactness axiom 5
f-phantom map 25 61 75
Faithful functor 440
Fill-in map 454
Filtered indexing category 446
Finite (graded) algebra 188
Finite spectrum 24 160
Finite type 25 170
Finitely extended module 223
Finitely generated module 171
Finitely presented module 171
Free module 171
Free through a degree 171
Frobenius algebra 188
Frobenius category 188
Full functor 440
Full subcategory 440
Function spectrum 65
Generalized Eilenberg — MacLane spectrum 86
Generators of a full subcategory 440
Genus 160
Graded category 442
Graded k-module 169
Graded weak cogenerator 221 443
Graded weak generator 31 291 443
| Higher operation associated to a complex 267
Homology functor 46
Homotopic maps 4
Homotopy category of CW-compiexes 4
Homotopy equivalence 4 23
Homotopy finite spectrum 44
Homotopy functor 46
Homotopy groups of a spectrum 44
Hopf algebra 185
Hurewicz isomorphism theorm 91
Hurewicz map 89
Idempotent functor 440
Indexing category 443
Injective dimension 177 196 201
Isomorphism mod torsion 114
Isomorphism of categories 441
K-invariant 72
Kernel 445
Kunneth formula 89
Large category 439
Large set 439
Left lexicographic order 238
Lightning flash module 317
LIMIT 152 221 287 444
Loop functor 207 442
Mapping cone 3
Mapping sequence 4
Milnor basis 228
Minimal period 224
Minimal weak colimit 36 73
Minimum resolution 174
Mittag-Leffler condition 448
Module over a graded algebra 170
Module over a hopf algebra 186
Module spectrum 47 359
Moore spectrum 34
n-realizable map 272
n-realizable module 271
n-stage splitting of a module 271
Normal subalgebra 172
Octahedral axiom 466
Opposite category 440
p-algebra 193 235 240
P-invariant 391
P-local module or spectrum 374
p-primary component 161
Periodic spectrum 292
Phantom map 72 98
Poincare algebra 188
Postnikov tower 71
Pro  -completion 132
PRODUCT 444
Product category 443
Profile function 232
Projective cover 172
Projective dimension 177 196 201
Pullback 444
Pushout 444
Rational localization 113
Realizable module 257 376
Replete category 440
Representable functor 11 46 59 441
Ring spectrum 47
Semi-triangulated category 217 286 453
Shift suspension 170 442
Small category 439
Small object 5 444
Small set 439
Small skeleton of a category 43 442
Smallness condition 107 451
Smash product 3 22 186 314
Spectrum 20 82
Sphere spectrum 23
Stability isomorphism 209 284
Stable (co)fibration 206 282
Stable boundedness 221 291 398
Stable category 205 280
Stable commuting diagram 205
Stable equivalence 205 280
Stable extension 60 442
Stable functor 442
Stable homotopy category 20
Stable homotopy groups 11 264
Stable natural transformation 5 10 60 442
Stable operation 6 250
Stable ring spectrum 359
Stable suspension 283
Stable triangle 217 285
Stable triviality 205 280
Steenrod algebra 228 239 250
Sub triangulated category 455
Support 389
Suspension functor 3 20 442
Suspension spectrum 82
Tensor algebra 172
Tensor category 124 149 443
Thom spectrum 82
Triangulated category 408 453
Twist map 171
Type 374
Type M< ,  > or X< , > 372 374 431
Type M<r, s> 322
Type X[m, n] 41
Universal coefficient theorem 88
Unstable A-module 246 277
Unstable exact triangle 4
Weak (co)limit 35 70 444
Weak (graded) generator 5 31.
Weak dimension 177 196 201
wedge 3
Wedge axiom 5
Whitehead theorem 91 320 335
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