ScalingStacks

Proposition 3.10. There is a weight structure $w$ on $\operatorname{DTM}_{G}(k,\mathbb{Q})$ such that

	$\displaystyle M\in\operatorname{DTM}_{G}(k,\mathbb{Q})^{w\geq 0}$	$\displaystyle\iff\operatorname{For}(M)\in\operatorname{DTM}(k,\mathbb{Q})^{w\geq 0}\text{ and }$
	$\displaystyle M\in\operatorname{DTM}_{G}(k,\mathbb{Q})^{w\leq 0}$	$\displaystyle\iff\operatorname{For}(M)\in\operatorname{DTM}(k,\mathbb{Q})^{w\leq 0}.$