ScalingStacks

Definition 4.1. The triangulated category of Springer motives $\operatorname{DM}^{Spr}_{G}(\mathcal{N},\mathbb{Q})$ is the full subcategory of $\operatorname{DM}_{G}(\mathcal{N})$ generated by $\widehat{\mathcal{T}}^{Spr}$ with respect to isomorphism, direct summands and triangles,

$$\operatorname{DM}^{Spr}_{G}(\mathcal{N},\mathbb{Q})=\langle\widehat{\mathcal{T}}^{Spr}\rangle_{\cong,\inplus,\Delta}\subset\operatorname{DM}_{G}(\mathcal{N}).$$