For a strongly inacessible cardinal $\kappa$, we investigate the relationships between following ideals: - ideal of meager sets in ${<}\kappa$-box product topology "null" sense [Sh:1004] (arXiv:1202.5799) nowhere stationary subsets (naturally defined) set $S_{\rm pr}^\kappa \subseteq \kappa$. In particular, analyse provable inequalities characteristics for these ideals, and give consistency res...