Example 2.1 (0MU8) · ScalingStacks

0MU8

Example 2.1. Let $R$ be a chain DGA. Let $\mathcal{D}(R)$ be the derived category of DG $R$ -modules, see [6], and define a pair of subcategories of $\mathcal{D}(R)$ as follows:

	$\displaystyle\mathcal{X}$	$\displaystyle=$	$\displaystyle\{M\in\mathcal{D}(R)\ \|\ H^{i}(M)=0\textnormal{ for }i>0\},$
	$\displaystyle\mathcal{Y}$	$\displaystyle=$	$\displaystyle\{M\in\mathcal{D}(R)\ \|\ H^{i}(M)=0\textnormal{ for }i<0\}.$

It is easy to show that the pair $(\mathcal{X},\mathcal{Y})$ forms a $t$ -structure on $\mathcal{D}(R)$ . Again, this $t$ -structure is non-degenerate and its heart consists of DG $R$ -modules whose cohomology is concentrated in degree zero.