Letters in Mathematical Physics
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.
Category of relations, Cohomology, Frobenius algebra, Groupoid, Simplicial set, Topological quantum field theory
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Mehta, Rajan Amit and Zhang, Ruoqi, "Frobenius Objects in the Category of Relations" (2020). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.