Descent and forms of tensor categories
  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. 
Pavel Etingof and Shlomo Gelaki
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