RATIONAL HOMOTOPY THEORY: THE GENERAL NILPOTENT CASE (SIMPLICIAL SETS, DG COALGEBRAS).
Item
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Title
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RATIONAL HOMOTOPY THEORY: THE GENERAL NILPOTENT CASE (SIMPLICIAL SETS, DG COALGEBRAS).
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Identifier
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AAI8713795
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identifier
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8713795
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Creator
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SEARL, JAMES EDWIN.
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Date
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1987
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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Let S(,o) be the category of reduced simplicial sets and C the category of commutative DG coalgebras over k (k a field of characteristic 0). A pair of adjoint functors (UNFORMATTED TABLE FOLLOWS).;(VBAR) (VBAR).;S(,o) (DBLARR) C.;S.;(TABLE ENDS).;is constructed ((VBAR) (VBAR) is the realization and S the singular functor) which induce an adjunction between the homotopy categories. With k = Q, the unit for the adjunction when restricted to nilpotent spaces gives a Q-localization and when restricted further to rational, nilpotent spaces gives an isomorphism. On the homotopy categories, the realization functor when restricted to the replete subcategory of rational, nilpotent spaces (and corestricted to its image) gives an equivalence of categories. This generalizes the equivalence result of Quillen for simply connected spaces. It also removes the homology finiteness conditions which were imposed by Neisendorfer to relate the homotopy category of spaces to that of coalgebras (via the Bousfield-Gugenheim equivalence for spaces and algebras). The realization functor (VBAR) (VBAR):S(,o) (--->) C is characterized by three basic properties in the sense that any functor F:S(,o) (--->) C which has these basic properties will also yield a Q-localization and give an equivalence of categories as was obtained using (VBAR) (VBAR).
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Mathematics
