  We consider analogues of the Bernstein-Gelfand-Gelfand resolution in a
highest weight category $\mathscr{P}$. We prove the resulting category of
complexes is a chain-level lift of the heart of the constructible $t$-structure
on its bounded derived category $D^b(\mathscr{P})$. In particular, an object
admits a Bernstein-Gelfand-Gelfand resolution if and only if a certain
$\operatorname{Ext}$ vanishing with costandard objects holds. These results
appear to be new even for Category $\mathscr{O}$.
