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We introduce a categorical version of the Bost-Connes (BC) system, following a general construction of C*-tensor categories going back to Zhu. The fusion ring of our categorical BC-system maps canonically onto the Hecke algebra underlying the BC-system, but contains further structure. We give a presentation in terms of generators and relations, and discuss the structure of its KMS-states. In contrast to the classical BC-system one obtains a complete symmetry between positive and negative temperatures. We also hint at the possibility of studying KMS-states from a categorical point of view.