Thomason Trobaugh Higher Algebraic K-theory Pdf Download


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Thomason,,(19521995).,,Baum,,,,P.,,,,Fulton,,,,W.,,,,Quart,,,,G.:,,,Lefschetz,,,Riemann,,,Roch,,,for,,,singular,,,varieties.,,,As,,,it,,,is,,,known,,,that,,,two,,,categories,,,with,,,cofibrations,,,and,,,weak,,,equivalences,,,having,,,equivalent,,,homotopy,,,categories,,,may,,,have,,,distinct,,,K-theory,,,[12],,,,Theorem,,,3.3,,,is,,,probably,,,the,,,strongest,,,statement,,,one,,,can,,,expect.Several,,,related,,,results,,,can,,,be,,,found,,,in,,,the,,,literature,,,,all,,,of,,,them,,,also,,,exploiting,,,more,,,structure,,,than,,,just,,,the,,,cofibrations,,,and,,,the,,,weak,,,equivalences.,,,In,,,a,,,recent,,,preprint,,,[11,,,,A.2,,,Theorem],,,Schlichting,,,shows,,,that,,,Waldhausen's,,,original,,,hypothesis,,,on,,,the,,,existence,,,of,,,a,,,cylinder,,,functor,,,can,,,be,,,replaced,,,by,,,a,,,weaker,,,condition,,,of,,,(non-functorial),,,factorization,,,of,,,maps.Our,,,approach,,,is,,,to,,,replace,,,additionally,,,the,,,approximation,,,property,,,App2,,,of,,,the,,,Approximation,,,Theorem,,,[16,,,,Theorem,,,1.6.7],,,by,,,a,,,weaker,,,condition.,,,Invent.,,,Examples,,are,,provided,,by,,the,,category,,of,,simplicial,,sets,,or,,by,,categories,,of,,spectra,,based,,on,,simplicial,,sets,,like,,symmetric,,spectra,,[6].Another,,interesting,,application,,is,,Theorem,,3.3.,,And,,,,they,,,,are,,,,asked,,,,to,,,,contain,,,,all,,,,cofibrant,,,,objects,,,,of,,,,the,,,,model,,,,categories,,,,that,,,,are,,,,weakly,,,,equivalent,,,,to,,,,an,,,,object,,,,of,,,,the,,,,subcategory.,,,,

vol.,,Thomason,,,,and,,,,Trobaugh,,,,[13,,,,,Theorem,,,,1.9.8],,,,show,,,,that,,,,a,,,,functor,,,,of,,,,“complicial,,,,biWaldhausen,,,,categories”,,,,induces,,,,an,,,,equivalence,,,,in,,,,the,,,,algebraic,,,,K-theory,,,,if,,,,it,,,,induces,,,,an,,,,equivalence,,,,of,,,,homotopy,,,,categories.,,,,(ed.),,,,Algebraic,,,,topology,,,,and,,,,algebraic,,,,K-theory.,,,,Screen,,,reader,,,users,,,,click,,,here,,,to,,,load,,,entire,,,articleThis,,,page,,,uses,,,JavaScript,,,to,,,progressively,,,load,,,the,,,article,,,content,,,as,,,a,,,user,,,scrolls.,,,Further,,,,reading[edit].,,,,Stud.,,,,,vol.,,,,Citing,,,,articles,,,,(0),,,,This,,,,article,,,,has,,,,not,,,,been,,,,cited.,,,,

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