Frobenius Objects in the Category of Relations

Authors

Rajan Amit Mehta, Smith CollegeFollow
Ruoqi Zhang, Smith College

Document Type

Article

Publication Date

7-1-2020

Publication Title

Letters in Mathematical Physics

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.

Keywords

Category of relations, Cohomology, Frobenius algebra, Groupoid, Simplicial set, Topological quantum field theory

Volume

110

Issue

7

First Page

1941

Last Page

1959

DOI

10.1007/s11005-020-01281-1

ISSN

03779017

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit and Zhang, Ruoqi, "Frobenius Objects in the Category of Relations" (2020). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/88