We show that direct limit completions of vertex tensor categories inherit vertex and braided tensor category structures, under conditions that hold for example for all known Virasoro and affine Lie algebra tensor categories. A consequence is that the theory of vertex operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid and non-degenerate vertex tensor categories of certain modules for both the affine vertex superalgebra of 𝔬𝔰𝔭(1|2) and the N = 1 super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.

中文翻译：

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顶点张量类别的直接极限补全

我们展示了顶点张量类别的直接极限完成继承了顶点和编织张量类别结构，例如在所有已知的 Virasoro 和仿射李代数张量类别的条件下。结果是顶点算子（超）代数扩展的理论也适用于无限阶扩展。作为一个应用程序，我们将某些模块的刚性和非退化顶点张量类别联系起来，用于仿射顶点超代数𝔬𝔰𝔭(1|2)和ñ = 1超级 Virasoro 代数通过某些陪集到 Virasoro 代数模块的类别。