2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69087We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-$\mathbb Q$-factorial toric varieties. So, our theory seems to be quite different from Reid's original combinatorial toric Mori theory. We also explain various examples of non-$\mathbb Q$-factorial contractions, which imply that the $\mathbb Q$-factoriality plays an important role in the Minimal Model Program. Thus, this paper completes the foundations of the toric Mori theory and show us a new aspect of the Minimal Model Program.21 pages; typos were corrected, new remarks were addedAlgebraic Geometry14M25; 14E30text