  Recently, several authors have adopted new alternative approaches in the
study of some classical notions of modules. Among them, we find the notion of
subprojectivity which was introduced to measure in a way the degree of
projectivity of modules. The study of subprojectivity has recently been
extended to the context of abelian categories, which has brought to light some
interesting new aspects. For instance, in the category of complexes, it gives a
new way to measure, among other things, the exactness of complexes. In this
paper, we prove that the subprojectivity notion provides a new sight of
null-homotopic morphisms in the category of complexes. This will be proven
through two main results. Moreover, various results which emphasize the
importance of subprojectivity in the category of complexes are also given.
Namely, we give some applications by characterizing some classical rings and
establish various examples that allow us to reflect the scope and limits of our
results.
