  In the context of categories equipped with a structure of nullhomotopies, we
introduce the notion of homotopy torsion theory. As special cases, we recover
pretorsion theories as well as torsion theories in multi-pointed categories and
in pre-pointed categories. Using the structure of nullhomotopies induced by the
canonical string of adjunctions between a category A and the category Arr(A) of
arrows, we give a new proof of the correspondence between orthogonal
factorization systems in A and homotopy torsion theories in Arr(A), avoiding
the request on the existence of pullbacks and pushouts in A. Moreover, such a
correspondence is extended to weakly orthogonal factorization systems and weak
homotopy torsion theories.
