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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