830 Index algebraic, 803 homology, 508 K¨ unneth theorem, 487, 488 algebraic, 803 homology, 509 Lebesgue Number Lemma, 77 left adjoint, 26 left derived functor, 269 left homotopic, 266 left homotopy, 90 left lifting property, 121 Leibniz rule, 653 length, 237 Leray-Hirsch theorem, 674 Leray-Serre spectral sequence, 74 relative, 662 lifting functor, 156 lifting function, 109 dual, 103 uniqueness, 140 lifting problem, 14 lim1 cohomology, 466 limit, 15, 31, 32 3 × 3 diagram, 42 commute with adjoint, 35 naturality, 34 pullback, 36 limit ordinal, 809 linear, 75, 295, 343 local section, 330 localization, 268 localized at, 723 localized away, 723 locally finite, 370 locally trivial bundle, 324 long A-cone decomposition, 239 long cofiber sequence, 200 long fiber sequence, 202 loop map homotopy pullback, 249 loop operation, 578 loop space, 67, 84, 577, 738 free, 141 group object in T∗, 87 homotopy pullback, 189 Lusternik-Schnirelmann category, 251, 252, 555, 713 cone length, 251 Ganea criterion, 254 homotopy invariance, 251 homotopy pushout, 253 Hopf invariant, 445 Lusternik-Schnirelmann cover, 250, 555 mapping cone, 256 of a map, 252 of CW complexes, 253 product, 256 manifold, 497 map finite type, 807 pointed, 60 map under, 94 mapping cone, 130 unpointed, 130 mapping cylinder, 111 in map(T◦), 115 pointed, 125 mapping space, 54 and colimits, 57 and limits, 57 cofibration, 105, 134 fibration, 133, 135 pointed, 61 well-pointed, 126 mapping torus, 179 Mather cube, 305, 395, 594, 627 matrix, 20, 421 Mayer-Vietoris cofiber sequence, 210 exact sequence, 465, 501 fiber sequence, 210 measured path, 374 Milnor sign convention, 413, 418 minimal, 739, 741 minimal model, 740 Mislin genus, 734 Mittag-Leffler, 775 model category, 89, 99, 261, 262 module, 789 graded, 796 moment, 537 monoid object, 21, 227 monster, 423, 499, 578 Moore homotopy, 376 Moore loops, 374 Moore path, 374 based, 374 Moore space, 425 cohomology of, 470 cohomology operation, 567 homology, 567 maps between, 568 Moore suspension, 379 morphism, 5 in pointed category, 20 matrix representation, 807 trivial, 19 multiplication, 226 multiplicative, 476, 608 multiplicative cohomology theory, 586

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