ScalingStacks

Definition 4.21. For a $K$-linear additive category $\mathcal{C}$, the Chern character is the $K$-linear map

$$h_{\mathcal{C}}\colon K_{0}(\mathcal{C})\otimes_{\mathbb{Z}}K\to\mathrm{HH}_{0}(\mathcal{C}),\quad[x]\otimes 1\mapsto[\operatorname{Id}_{x}\colon x\to x]$$