  We develop the theory of exact completions of regular $\infty$-categories,
and show that the $\infty$-categorical exact completion (resp. hypercompletion)
of an abelian category recovers the connective half of its bounded (resp.
unbounded) derived $\infty$-category. Along the way, we prove that a finitely
complete $\infty$-category is exact and additive if and only if it is
prestable, extending a classical characterization of abelian categories. We
also establish $\infty$-categorical versions of Barr's embedding theorem and
Makkai's image theorem.
