  We extend some classical results of Bousfield on homology localizations and
nilpotent completions to a presentably symmetric monoidal stable
$\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete
$t$-structure. If $E$ is a homotopy commutative algebra in $\mathscr{M}$ we
show that $E$-nilpotent completion, $E$-localization, and a suitable formal
completion agree on bounded below objects when $E$ satisfies some reasonable
conditions.
