Homological algebra and (semi)stable homotopy (Q674473)

The preceding paper [\textit{A. Heller}, ``Stable homotopy theories and stabilization'', J. Pure Appl. Algebra 115, No. 2, 113-130 (1996; Zbl 0868.18001)] considers cocontinuous/continuous stabilizations of regular/coregular homotopy theories. As well as a universal problem of spectra, the same leads, for abelian categories to the construction of chain complexes. For a (complete and cocomplete) abelian category \({\mathcal A}\) and a small category \({\mathcal C}\), the 2-functors with values in the homotopy category of chain complexes over \({\mathcal A}^{\mathcal C}\) provide homotopy theories which are in a sense universal stabilization or semistabilization.