Given an arbitrary countably generated rigid C*-tensor category, we construct a fully-faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital C*-algebra with unique trace. The C*-algebras involved are built from the category using the GJS-construction introduced in arXiv:0911.4728 and further studied in arXiv:1208.5505 and arXiv:1401.2486. Out of this category of Hilbert C*-bimodules, we construct a fully-faithful bi-involutive strong monoidal functor into the category of bi-finite spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the functor constructed in arXiv:1208.5505

中文翻译：

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刚性 C*-张量类别作为 GJS C*-代数上的双模的实现

给定一个任意可数生成的刚性 C*-张量类别，我们在一个简单、精确、可分离、具有唯一迹的单位 C*-代数上，在有限生成的射影双模子类别上构造一个完全忠实的双对合强幺半群函子。所涉及的 C*-代数是使用 arXiv:0911.4728 中引入的 GJS 构造从类别构建的，并在 arXiv:1208.5505 和 arXiv:1401.2486 中进一步研究。从这类 Hilbert C*-bimodules 中，我们构建了一个完全忠实的双对合强幺半群函子，在一个插值的自由群因子上将其构建为双有限球双模的范畴。这两个函子的组合恢复了在 arXiv:1208.5505 中构造的函子