  Assume ZFC. Let $\kappa$ be a cardinal. A ${<\kappa}$-ground is a transitive
proper class $W$ modelling ZFC and such that $V$ is a generic extension of $W$
via a forcing $\mathbb{P}\in W$ of cardinality ${<\kappa}$. The $\kappa$-mantle
is the intersection of all ${<\kappa}$-grounds. We prove that certain partial
choice principles in the $\kappa$-mantle are the consequence of $\kappa$ being
inaccessible/weakly compact, and some other related facts.
