824 Index boundary, 295 boundary map, 241, 543, 798 product, 243 bounded below, 795 Bousfield equivalent, 725 Brown Representability Theorem, 490 bundle isomorphism, 335 bundle map, 324, 334 bundle of groups, 625 Cartan formula, 525, 533 category, 5 discrete, 33 Lusternik-Schnirelmann, 250, 555 pointed, 18 category of maps, 91 cell closed, 47 open, 47 cellular action, 217 Cellular Approximation Theorem, 299 1-dimensional, 74, 78 cellular chain complex product space, 549 cellular cochain complex, 543 cellular inequality, 759, 764 cellular map, 48, 78, 299 cellular replacement, 340 existence, 355 uniqueness, 354 chain algebra, 550, 653 chain complex, 543, 798 chain map, 544, 798 change of fiber, 335 characteristic map, 47 characterization acyclic cofibrations, 121, 129 acyclic fibrations, 121, 129 cofibrations, 121, 129 fibrations, 121, 129 Clark, 18 class, 5 classified, 370 classifying space, 177, 370 closed under homotopy limits, 409 under smash, 762 under weak homotopy equivalence, 409 under wedge, 762 closed class, 759, 764 closed cofibration, 104 closed under suspension, 238, 762 closed under wedges, 238 clutching, 603 map, 603 co-H-space, 228 retract, 228 suspension, 359 coagumentation, 722 coalgebra, 803 homomorphism, 804 coboundary map, 543 cocartesian, 196 cochain complex, 543, 798 cocommutative, 25, 804 cocomplete, 262 cocycles, 544 coefficient group, 462, 500 coefficient transformations, 516 coefficients, 427, 461 coend, 346 coequalizer, 38 cofiber, 130 homotopy invariance, 163 homotopy pushout, 184 of a composite, 216 of contractible subspace, 132 of projection map, 223 of trivial map, 194 standard, 130, 131 unpointed, 131 cofiber sequence, 131, 460 exactness, 131 long sequence, 201 Mayer-Vietoris, 210 cofibrant, 101, 147, 148, 264 cofibrant diagram characterization, 158 cofibrant replacement, 150 prepushout diagrams, 148 cofibration, 99, 100, 262 acyclic, 121 adjoint pair, 129 closed, 104 composition, 100 converting to, 112 exact sequence, 201, 202 exactness, 130 mapping space, 105, 134 pointed, 122 product, 106 pushout, 103 retract, 121 trivial, 121 cofibrations inclusion maps, 101 pushouts, 103 cofinal subdiagram, 40 cofinality, 809 cogroup object, 23 cocommutative, 25 Cohen-Moore-Neisendorfer lemma, 215 coherent homotopies, 92
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