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arXiv · 2403.07768

Higher Witt Groups for 2-Categories I: Centralizers

Hao Xu
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Abstract

In this article, we investigate monoidal, braided, sylleptic centralizers of monoidal, braided, sylleptic 2-functors. We specifically focus on multifusion 2-categories and show that monoidal, braided, sylleptic centralizers are multifusion again, via studying the corresponding enveloping algebras. We provide a characterization of the non-degeneracy condition for monoidal, braided, and sylleptic fusion 2-categories, via vanishing of their centers. Applying Double Centralizer Theorems, we establish the relationship between monoidal, braided, symmetric local modules and free modules. In particular, we obtain factorization properties of non-degenerate monoidal, braided, and sylleptic fusion 2-categories. Main results in this article will be used to study higher Witt equivalences of non-degenerate monoidal, braided, sylleptic 2-categories in the sequential articles.

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Hao Xu. 2025-03-14. Higher Witt Groups for 2-Categories I: Centralizers. https://arxiv.org/abs/2403.07768

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