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

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