  The Artin stack $\mathcal M_n$ of $0$-dimensional sheaves of length $n$ on
$\mathbb A^3$ carries two natural d-critical structures in the sense of Joyce.
One comes from its description as a quotient stack
$[\textrm{crit}(f_n)/\textrm{GL}_n]$, another comes from derived deformation
theory of sheaves. We show that these d-critical structures agree. We use this
result to prove the analogous statement for the Quot scheme of points
$\textrm{Quot}_{\mathbb A^3}(\mathscr O^{\oplus r},n) =
\textrm{crit}(f_{r,n})$, which is a global critical locus for every $r>0$, and
also carries a derived-in-flavour d-critical structure besides the one induced
by the potential $f_{r,n}$. Again, we show these two d-critical structures
agree. Moreover, we prove that they locally model the d-critical structure on
$\textrm{Quot}_X(F,n)$, where $F$ is a locally free sheaf of rank $r$ on a
projective Calabi-Yau $3$-fold $X$.
  Finally, we prove that the perfect obstruction theory on
$\textrm{Hilb}^n\mathbb A^3=\textrm{crit}(f_{1,n})$ induced by the Atiyah class
of the universal ideal agrees with the critical obstruction theory induced by
the Hessian of the potential $f_{1,n}$.
