  We compute the Bousfield localizations and Bousfield colocalizations of
discrete model categories, including the homotopy categories and the algebraic
$K$-groups of these localizations and colocalizations. We prove necessary and
sufficient conditions for a subcategory of a category to appear as the
subcategory of fibrant objects for some such model structure. We also prove
necessary and sufficient conditions for a monad to be the fibrant replacement
monad of some such model structure.
