Index
acyclic, 140
algebraic /f-theory, 103-126
of finitely free modules, 114
of spaces, 125-126
Quillen, 114
approximation theorem. 107
Atiyah-Hirzebruch spectral sequence, 80
Atiyah-Segal completion theorem, 166
Baas-Sullivan theory, 91
bar construction, 88, 136, 162, 172, 173,
186-187, 209-214
bar construction spectral sequence, 89
bimodule, 59-61, 65-66, 68, 128, 130
Bott element, 166
Bousfield localization, 155-166
Brown's representability theorem, 58, 75,
76
Brown-Peterson spectrum, 101
category with w-cofibrations, 103
cell algebra, 62
and Bousfield localization, 160, 166
see also g-cofibrant algebra
cell and CW L-spectra, 18, 22
cell and CW modules, 33-34, 54-58, 63,
147-149, 184
and extended powers, see extended power
and extension of scalars, 61, 62
and function modules, 67
and smash products, 60, 61, 69
and symmetric powers, see symmetric
power
cell commutative algebra
and Bousfield localization, 160, 166
see also g-cofibrant commutative alge-
bra
cell T-algebra, 143-144, 147
cellular approximation, 57
cellular chain complex, 75, 79
center, 128
central map, 128
change of universe, 14, 232
CHP, see covering homotopy property
cobar construction. 187
cobase change, 152
cocompleteness, of category of
Aoo ring spectra, 47-49
commutative ^-algebras. 47-49
commutative 5-algebras. 47-49
Eoc ring spectra, 47-49
L-spectra, 18
^-algebras, 47-49
/?-modules, 51
5-algebras, 47-49
5-modules, 32
spectra, 10
cocompleteness, topological, 131
coconnective, 73
coend, 179
coequalizer
homotopy, see double mapping cylin-
der
see also homotopy colimit
reflexive, see reflexive coequalizer
split, see split coequalizer
cofiber, 10, 92
cofiber sequence, 10, 75
and function module, 67, 79
and long exact sequences, 15, 23, 72,
73
and smash product, 23, 59
cofibration, 10, 140, 182, 187
Cofibration Hypothesis, 143
compact ^-module, 53, 55, 201
compact spectrum, 53
completeness, of category of
Aoc ring spectra. 40
commutative H-algebras, 40
commutative 5-algebras, 40
Eoc ring spectra, 40
L-spectra, 18
/^-algebras, 40
/^-modules, 51
5-algebras, 40
5-modules, 32
spectra, 10
completeness, topological, 131
completion, see Bousfield localization
complex /^-theory, see A'-theory
connective, 57
connective /C-theory, see A'-theory
cotensor, 131
counital L-spectra, see mirror image
covering homotopy property, 10, 140
see also fibration
cyclic bar construction, 172
cylinder axiom, 107
cylinder construction, 191-195
cylinder functor, 107
cylinder object, 108, 144
degeneracy subspectrum, 182
247
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