On Examples and Classification of Frobenius Objects in Rel
Ivan Contreras, Adele Long, Sophia Marx, Rajan Amit Mehta
TL;DR
This paper introduces new examples of Frobenius objects in the category of sets and relations, classifies small cases, and explores their surface invariants via TQFT partition functions.
Contribution
It provides novel examples of Frobenius objects in Rel, including a groupoid with a twisted counit and conjugacy classes, and classifies small Frobenius objects.
Findings
New Frobenius objects in Rel identified
Classification of Frobenius objects with 2 or 3 elements
Surface invariants computed using TQFT partition functions
Abstract
We give some new examples of Frobenius objects in the category of sets and relations . One example is a groupoid with a twisted counit. Another example is the set of conjugacy classes of a group. We also classify Frobenius objects in with two or three elements, and we compute the associated surface invariants using the partition functions of the corresponding TQFTs.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Finite Group Theory Research