By [Lur17, Rem. 1.3.1.11], the homotopy 1-category \(h_1{\mathbf K}^b(\mathcal A)\), recalled in subsection A.2.1, is the chain homotopy category \(\mathrm{K}^b(\mathcal A)\) in the sense of definition 2.2.2. Note that, unlike the notion of derived category, which can only be defined for abelian categories, the stable \(\infty\)-category \({\mathbf K}^b(\mathcal A)\) is defined for any (possibly non-abelian) additive category \(\mathcal A\).
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2