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