Kerodon

Example 2.5.4.9 (The Homotopy Category of Chain Complexes). Let $\operatorname{\mathcal{A}}$ be an additive category, and let $\operatorname{Ch}(\operatorname{\mathcal{A}})$ be the differential graded category of chain complexes with values in $\operatorname{\mathcal{A}}$ (Example 2.5.2.5). Then the homotopy category of $\operatorname{Ch}(\operatorname{\mathcal{A}})$ in the sense of Construction 2.5.4.6 agrees with the homotopy category $\operatorname{hCh}(\operatorname{\mathcal{A}})$ introduced in Construction 2.5.0.9.