We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain cohomology classes in a compact oriented Riemannian manifold.

中文翻译：

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关系范畴中的 Frobenius 对象

我们根据单纯集对关系范畴中的 Frobenius 对象进行刻画。该结果概括了 Heunen、Contreras 和 Cattaneo 的结果，表明关系范畴中的特殊匕首 Frobenius 对象与 groupoids 对应。作为额外的例子，我们在关系范畴中构造一个 Frobenius 对象，其元素是紧致的黎曼流形中的某些上同调类。