ScalingStacks

Proof. By (3.2) the collection of objects in the $\operatorname{DTM}(k,\mathbb{Q})^{w=0}$ is negative. Moreover $\operatorname{DTM}(k,\mathbb{Q})$ is idempotent closed and generated by $\operatorname{DTM}(k,\mathbb{Q})^{w=0}$. Now the statement follows from Proposition 2.4. ∎