Abstract
Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14], the infinity-gon of [12], and the m-cluster category of type A ∞ (m ≥ 3) [13] are examples of this construction as well as some new examples such as the cluster category of ℤ2. An extension of this construction and further examples are given in [16].
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