Index 827 split, 517 exactness unreduced homology, 500 excess, 537, 538, 705 Excision Axiom, 461 exhaustive, 612 exponent, 636, 745 exponential law, 54, 55, 57, 65, 81, 84, 791 for pairs, 59 pointed, 62 Ext-p-complete, 735 extend to cone, 82 extension, 100 functor, 156 extension problem, 14 exterior algebra, 793, 797 graded, 796 exterior product homology, 508 with respect to a pairing, 632 external cohomology product for cartesian products, 475 external product, 427, 473 cohomology, 474 F-algebra, 553 f-equivalence, 724 f-local, 724 face, 342 face map, 342 factors through, 4 fat wedge, 251 fiber, 108, 131, 337 homotopy, 131 of a composite, 216 of trivial map, 194 suspension, 453 fiber bundle, 334 fiber sequence, 132 exactness, 132 homotopy pullback, 189 long sequence, 202 Mayer-Vietoris, 210 fiber-cofiber construction, 395 fibrant, 110, 168, 264 pointed diagram, 171 fibrant replacement, 168, 171 fibration, 99, 108, 262, 325 adjoint pair, 129 converting to, 113 evaluation, 109 mapping space, 133, 135 orientable, 203 path space, 109 pointed, 123 product, 110 pullback, 110 retract, 121 sequence, 132 trivial, 110 unpointed, 123 filtered R-algebra, 609 filtered map, 608 filtered space, 607 filtration, 605, 607, 613 ascending, 607, 609 descending, 609 finite, 612 of an element, 613 filtration degree, 612 filtration quotients, 605, 610 finite, 30 finite type, 807 finite-type map, 422 map of wedges, 469 wedge, 762 Five Lemma, 795 fixed point, 417 fixed points space of, 217 folding map, 17 forgetful functor, 10 free, 218 free abelian group, 27 free graded commutative algebra, 797 free loop space, 141, 259 free module, 790 free product, 290 free resolution, 386, 425 Freudenthal Suspension Theorem, 383 dual, 403 in dimension 1, 388 functor, 8 contravariant, 9 covariant, 8 extension, 156 forgetful, 10 homotopy, 80 lifting, 156 preserve homotopy colimit, 174 preserve homotopy limit, 174 represented, 11 fundamental class, 490 fundamental group, 9 fundamental groupoid, 205 Fundamental Lifting Property pointed, 128 unpointed, 118 Fundamental Theorem of Algebra, 419, 554 G-CW complex, 217 G-CW replacement, 219

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