Functorially finite hearts, simple-minded systems in negative cluster categories, and noncrossing partitions

Raquel Coelho Simoes, David Pauksztello, David Ploog with an appendix by Raquel Coelho Simoes +1

Let $Q$ be an acyclic quiver and $w\ge 1$ 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…