Example 2.2 (0MU9) · ScalingStacks

0MU9

Example 2.2. Let $R$ be a simply connected cochain DGA. Let $\mathcal{D}(R)$ be the derived category of DG $R$ -modules and define a pair of subcategories of $\mathcal{D}(R)$ as follows:

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

It is easy to show that the pair $(\mathcal{A},\mathcal{B})$ forms a co- $t$ -structure on $\mathcal{D}(R)$ . As in Example 2.1, this co- $t$ -structure is non-degenerate and its coheart consists of DG $R$ -modules whose cohomology sits in degree zero.