Index
Page numbers in bold point to
A-cellular equivalence, 50, 50
yl-cellular object, 84, 84
A-cellular space, 51
A-colocal, see also iC-colocal and colocal
A-local, 8
A-local equivalence, 48
A-local object, 48
A-null object, 48
^-periodic, 8
Adams, J. F., 140
adjoint functors, 157-158
and lifting model category structures, 214,
224
between diagram categories, 224
adjointness, 165, 327
and corealizations, 326-331
and cosimplicial simplicial sets, 313
and realizations, 326—331
of coends and ends, 388
of mapping spaces, 7
of tensor product and exponentiation, 161
of total derived functors, 157
adjoint s
and lifting, 114
preserving cofibrations and fibrations, 115
No, 187
augmented functor, 139, 139-140, 264
augmented set of horns, 17, 73, 73, 85, 86,
89
and local objects, 17, 73
B, 254
basis of a free cell complex, 272, 272, 273,
274
bisimplicial homotopy lifting extension the-
orem, 334
bisimplicial set, 303-305
as a resolution, 335
cofibrant, 305
cofibration, 305
diagonal, 312, 312-315
isomorphic to realization, 313
weakly equivalent to the homotopy co-
limit, 398
definitions of the indexed terms.
diagonal of
fibrant, 336
different model category structures, 303
fibration, 336
homotopically constant
weakly equivalent to zero-th degree, 315
homotopy colimit
weakly equivalent to the diagonal, 398
latching object, 305
realization, 312, 312-315
isomorphic to diagonal, 313
Reedy fibrant, 335
weak equivalence of realizations, 315
boundary
of a cell, 37
of a free diagram, 299
as a colimit, 299
left adjoint to matching object, 299
of a free diagram of sets, 298
as a colimit, 298
of a set of maps, 298
bounding the size
of a set of maps, 236
of cell complexes, 236-237
Bousfield localization, 57, 57-69
and homotopic maps, 68, 69
and localization, 63
and properness, 65-68
and Quillen equivalences, 64
and Quillen functors, 58, 63
and Quillen pairs, 64
and resolutions, 61
existence, 71, 83
Bousfield, A. K., xi, xiii, 42, 57, 78, 397
Bousfield-Kan map, 397, 396-398, 427
weak equivalence, 397, 398, 427
Bousfield-Smith cardinality argument, 42-
46, 78-81
Brown, K. S., 129
6-(co)local Whitehead theorem, 55
C-colocal, 65
C-colocal equivalence, 48, 49
C-colocal object, 48, 49
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