832 Index principal cofibration, 237 principal ideal domain, 487, 801 product, 15, 17, 18 as functor, 16 flat, 223 infinite, 807 infinite weak product, 376 of CW complexes, 50 of group objects, 26 of groups, 17 of many objects, 18 of mapping cones, 224 of maps, 16 of sets, 17 pointed spaces, 62 product rule, 653 projections, 15 projective, 790, 799 projective resolution, 800 projective space, 51 cohomology, 470 cohomology algebra, 480 CW decomposition, 53 CW structure, 53 diagonal map, 482 fiber bundle, 325 infinite-dimensional, 52 truncated, 586 pullback, 36 composition of, 41 fibration, 110 product, 65 square, 36 punctured, 196 punctured n-cube, 405 pure quaternion, 420 pushout, 37 composition of, 40 of equivalence, 40 square, 37 wedge, 65 quadratic part, 740 quasi-isomorphism, 799 quasifibration, 347 quasiregular, 743 quaternions, 419 Quillen adjunction, 270 Quillen equivalence, 268, 270 quotient map, 49 R-algebra, 792 graded, 796 R-module graded, 795 rational homotopy theory, 797 rationalization, 733 rationally elliptic, 741 rationally hyperbolic, 741 reduced p powers, 527 reduced diagonal, 260, 476 reduced product type, 454 regular prime, 743 regular value, 415, 497 relation, 294 relative CW complex, 60 relative Sullivan algebra, 739 reparametrization, 73 represented cohomology, 460 represented functor, 11 represents, 614 resolving class, 409 respects homotopy, 71 retract, 7 of a map, 7 reverse, 74 reverse path, 73 Riemannian metric, 677 right adjoint, 26 right homotopic, 266 right homotopy, 90 right lifting property, 121 rigid concatenation, 374 rigidification, 178 root, 156 RPT complex, 454 RPT model, 455 Schubert symbol, 237 Second Cube Theorem, 398 section, 203 Ωf, 207 Serre class, 714 Serre cofibrations, 336 Serre exact sequence, 583 Serre fibration, 336, 337 sequence, 337 Serre filtration, 600, 601, 623 Serre model structure, 264 shape, 29, 30 shape diagram, 29 shear map, 229, 287 shift map, 39, 246, 465, 501 short exact sequence, 794 shuffle product, 688 simple category, 155 simple system, 704, 708 p-simple, 708 simplex, 295, 296 boundary, 295 standard, 295 simplex category, 348 simplicial complex, 296, 342 abstract, finite, 296

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