Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.
Descent and forms of tensor categories
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abstract
We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of forms. We also discuss the problem of categorification of weak fusion rings, and for the simplest families of such rings, determine which ones are categorifiable.
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Compact Semisimple Tensor 2-Categories are Morita Connected
Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.