Setup 5.1 (0MUV) · ScalingStacks

0MUV

Setup 5.1. Throughout this section, we shall consider the co- $t$ -structure of Theorem 4.1; that is, let $\mathcal{T}$ be a triangulated category with set indexed coproducts, suppose $S$ is a compact simply connected corigid object of $\mathcal{T}$ . Furthermore, assume that $\{\Sigma^{i}S\ |\ i\in\mathbb{Z}\}$ is a generating set for $\mathcal{T}$ . Then, by Theorem 4.1, the following is a non-degenerate co- $t$ -structure on $\mathcal{T}$ :

	$\displaystyle\mathcal{A}$	$\displaystyle=$	$\displaystyle\{X\in\mathcal{T}\ \|\ \textnormal{Hom}(S,\Sigma^{i}X)=0% \textnormal{ for }i<0\},$
	$\displaystyle\mathcal{B}$	$\displaystyle=$	$\displaystyle\{X\in\mathcal{T}\ \|\ \textnormal{Hom}(S,\Sigma^{i}X)=0% \textnormal{ for }i>0\}.$

Let $\mathcal{C}=\mathcal{A}\cap\mathcal{B}$ be the coheart of this co- $t$ -structure.