Definition 3.4.1. ([Lur17, Cons. 1.3.1.6 and Rem. 1.3.2.2]).
For an ordinary additive \(1\)-category \(\mathcal A\), we let \({\mathbf K}^b(\mathcal A):=N_{\mathrm{dg}}(\mathrm{Ch}^b(\mathcal A))\) denote the dg nerve of the dg category of bounded chain complexes in \(\mathcal A\).