Descent and forms of tensor categories

Details Descent and forms of tensor categories Descent and forms of tensor categories

2011-02-03

arxiv.org/abs/1102.0657v2

Mathematics

Quantum Algebra

22 pages; minor changes in Example 3.3, Proposition 3.7, Theorem 4.3(iv) and Theorem 4.6(iv)

Scientific paper

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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