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.
Theory and Applications of Categories, Vol. 10, 2002, No. 8, pp 162-179 http://www.tac.mta.ca/tac/volumes/10/8/10-08.dvi http://www.tac.mta.ca/tac/volumes/10/8/10-08.ps http://www.tac.mta.ca/tac/volumes/10/8/10-08.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/8/10-08.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/8/10-08.psTAC Home