Monoidal characterisation of groupoids and connectors

Gran, Marino;Heunen, Chris;Tull, Sean
(2020) Topology and Its Applications — Vol. 273, n° 15, p. 106966 (2020)

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  • Gran, MarinoUCLouvain
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  • Heunen, ChrisUniversity of Edinburgh
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  • Tull, SeanUniversity of Oxford
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Abstract
We study internal structures in regular categories using monoidal methods. Groupoids in a regular Goursat category can equivalently be described as special dagger Frobenius monoids in its monoidal category of relations. Similarly, connectors can equivalently be described as Frobenius structures with a ternary multiplication. We study such ternary Frobenius structures and the relationship to binary ones, generalising that between connectors and groupoids.
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Gran, M., Heunen, C., & Tull, S. (2020). Monoidal characterisation of groupoids and connectors. Topology and Its Applications, 273(15), 106966. https://doi.org/10.1016/j.topol.2019.106966 (Original work published 2020)