  There is a lattice of torsion theories in simplicial groups such that the
torsion/torsion-free categories are given by simplicial groups with truncated
Moore complex below/above a certain degree. We study the restriction of these
torsion theories to certain subcategories of simplicial groups. In particular,
we prove that the categories of D.Conduch\'{e}'s 2-crossed modules and Ashley's
crossed complexes in groups are semi-abelian and we give some descriptions of
their torsion theories. These examples of torsion theories also give rise to
new examples of pretorsion theories in the sense of A. Facchini and C.
Finocchiaro, as well as examples of torsion torsion-free theories (TTF
theories).
