  We clarify some results of Bagaria and Magidor \cite{MR3152715} about the
relationship between large cardinals and torsion classes of abelian groups, and
prove that (1) the Maximum Deconstructibility principle introduced in
\cite{Cox_MaxDecon} requires large cardinals; it sits, implication-wise,
between Vop\v{e}nka's Principle and the existence of an $\omega_1$-strongly
compact cardinal. (2) While deconstructibility of a class of modules always
implies the precovering property by \cite{MR2822215}, the concepts are
(consistently) non-equivalent, even for classes of abelian groups closed under
extensions, homomorphic images, and colimits.
