# Frobenius objects in the category of relations

## TL;DR

This paper characterizes Frobenius objects in the category of relations using simplicial sets, extending known correspondences with groupoids and providing new examples related to cohomology classes in manifolds.

## Contribution

It offers a simplicial set-based characterization of Frobenius objects in relations, generalizing previous groupoid correspondences and constructing novel examples from manifold cohomology.

## Key findings

- Frobenius objects characterized via simplicial sets.
- Extension of groupoid correspondence to broader Frobenius objects.
- Construction of Frobenius objects from cohomology classes in manifolds.

## Abstract

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.

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Source: https://tomesphere.com/paper/1907.00702