Abstract:We explicitly construct dual bimodules in a semistrict monoidal 2-category, using Frobenius algebra structure. The main result shows that a coherent dual of the underlying object can be promoted to a coherent dual of the bimodule, with zigzag 2-isomorphisms additionally require special Frobenius structures. We also prove that every special Frobenius algebra in $\mathbf{2Vect}$ is rigid, via a categorified Casimir object argument, and discuss the relationship between the Frobenius, rigid, special Frobenius, and separable algebra hierarchies.
From: Hao Xu [view email]
[v1]
Mon, 1 Jun 2026 10:36:38 UTC (911 KB)
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