Looking at the nCatLab page on chain complexes, it is implicitly assumed at the start of the page that one is working in an additive category. However, the only structure required to define chain complexes is that one be working in a pointed category, so that the notion of a zero morphism makes sense. However, I have not been able to find any papers which consider chain complexes even in categories such as preadditive or semiadditive categories, much less arbitrary pointed categories.
I understand that many of the results of homological algebra rely on an Abelian structure to work. Is it simply the case that non-additive categories don't have enough structure to yield any interesting results about these complexes? Or is there a concrete issue that prevents chain complexes from making sense at all in more general pointed categories? Do these issues still arise even when working in preadditive or semiadditive categories?