# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark 2.5.4.7. Passage from a differential graded category $\operatorname{\mathcal{C}}$ to its homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ can be regarded as a special case of Remark 2.1.7.4, applied to the lax monoidal functor

$\operatorname{Ch}(\operatorname{\mathbf{Z}}) \rightarrow \operatorname{Set}\quad \quad (C_{\ast }, d) \mapsto \mathrm{H}_0( C )$

with tensor constraints given by

$\mu _{C,D}: \mathrm{H}_0(C) \times \mathrm{H}_0(D) \rightarrow \mathrm{H}_0( C \boxtimes D) \quad \quad ( [x], [y] ) \mapsto [x \boxtimes y].$