Index

∞-connected, 279

∞-equivalence, 278

3 × 3 diagram, 166, 173

homotopy colimit, 166

homotopy limit, 173

A-cone decomposition, 238

A-module, 796

A-morphism, 94

abelianization, 388

abstract simplicial complex, 296, 342

action

naturality, 206

acyclic, 700, 799

acyclic cofibration, 121, 263

acyclic fibration, 121, 263

Adams operations, 697

´

Adem relations, 520, 533

adjoint, 26, 54

loop space, 207

suspension, 207

adjoint functors

and cofibrant diagrams, 151

cofibrations, 122

fibrations, 122

adjunction

counit, 28

unit, 28

admissible, 537, 538, 592, 705

for

h∗,

592

admissible map, 204

admissible path

for p, 204

admissible trivialization, 592

algebra

graded, 796

algebraic closure, 4

algebraic K¨ unneth map, 803

algebraic loop, 287

amalgamated free product, 291

antipodal map, 415, 472

antipode, 52

associated graded, 610

associative, 227, 475

augmentation, 780, 797

augmentation ideal, 780, 797

augmented algebra, 797

barycenter, 297

barycentric subsimplex, 297

base, 108

based maps, 60

basepoint, 19, 60

change, 211

of I, 67, 70

bidegree, 559, 587, 612, 653

bigraded, 612

bilinear, 790

Blakers-Massey theorem, 398

n-dimensional, 406

cellular, 769

geometric version, 401

mod Q, 445

Bockstein, 520, 567

map, 517

operation, 517

Borel construction, 220, 335

Borsuk-Ulam theorem, 566

Bott map, 692

Bott-Samelson theorem, 577

boundaries, 544, 798

823