ScalingStacks

Theorem 4.1. Let $𝒯$ be a triangulated category with set indexed coproducts. Suppose $S$ is a compact simply connected corigid object of $𝒯$. Further assume that $\{{\mathrm{\Sigma }}^{i}S|i\in \mathbb{Z}\}$ is a generating set in $𝒯$. Then the following forms a non-degenerate co-$t$-structure on $𝒯$:

	$𝒜$	$=$
	$ℬ$	$=$	$\{X\in 𝒯|\text{Hom}(S,{\mathrm{\Sigma }}^{i}X)=0\text{ for }i>0\}.$

Note that $ℬ=S^{{⟂}_{\mathrm{\infty }}}$.