Given an ordinary additive, idempotent complete \(1\)-category \(\mathcal A\), the \(\infty\)-category \({\mathbf K}^b(\mathcal A)\) has a canonical bounded weight structure with \({\mathbf K}^b(\mathcal A)_{\geq 0}\) the (dg nerve on the) full subcategory of chain complexes supported in non-negative homological degrees. The weight heart \({\mathbf K}^b(\mathcal A)^\heartsuit \simeq \mathcal A\) recovers the original additive \(1\)-category and its inclusion is the canonical functor \(\mathcal A\rightarrow{\mathbf K}^b(\mathcal A)\).
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2