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Colocalizations and their realizations as spectra

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Friedrich W. Bauer

Every chain functor $A_*$, admits a $L$-colocalization
$A^L_*$ which (in contrast to the case of
$L$-localizations) in general does not allow a
realization as a spectrum (even if $A_*$ stems from a spectrum
itself). The $[E, ]_*$- colocalization of A. K. Bousfield is
retrieved as a special case of a general colocalization process for
chain functors.

Keywords: Colocalizations, chain functors, realizations of chain functors as spectra.

2000 MSC: Primary: 55P60, 55N20; Secondary: 55U30, 55P42.

*Theory and Applications of Categories*, Vol. 10, 2002, No. 8, pp 162-179.

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