![]() ![]() Here we consider two flavours of categorified symmetries: one coming from noncommutative algebraic geometry where varieties themselves are replaced by suitable categories of sheaves another in which the gauge groups are categorified to higher groupoids. Nowdays many examples of symmetries of categorical flavor - categorical groups, groupoids, Lie algebroids and their higher analogues - appear in physically motivated constructions and faciliate constructions of geometrically sound models and quantization of field theories. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. ![]() Quantum field theory allows more general symmetries than groups and Lie algebras.
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