Let $Q$ be an acyclic quiver and $w \geqslant 1$ be an integer. Let $\mathsf {C}_{-w}({\mathbf {k}} Q)$ be the $(-w)$ -cluster category of ${\mathbf {k}} Q$ . We show that there is a bijection between simple-minded collections in $\mathsf {D}^b({\mathbf {k}} Q)$ lying in a fundamental domain of $\mathsf {C}_{-w}({\mathbf {k}} Q)$ and $w$ -simple-minded systems in $\mathsf {C}_{-w}({\mathbf {k}} Q)$ . This generalises the same result of Iyama–Jin in the case that $Q$ is Dynkin. A key step in our

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... proof is the observation that the heart $\mathsf {H}$ of a bounded t-structure in a Hom-finite, Krull–Schmidt, ${\mathbf {k}}$ -linear saturated triangulated category $\mathsf {D}$ is functorially finite in $\mathsf {D}$ if and only if $\mathsf {H}$ has enough injectives and enough projectives. We then establish a bijection between $w$ -simple-minded systems in $\mathsf {C}_{-w}({\mathbf {k}} Q)$ and positive $w$ -noncrossing partitions of the corresponding Weyl group $W_Q$ .