Bruguières, Alain Noncommutative Tannaka theory. (Théorie tannakienne non commutative.) (French) Zbl 0808.18005 Commun. Algebra 22, No. 14, 5817-5860 (1994). The author extends the Tannaka-Krein results over a field to the noncommutative situation. More precisely, a 1-1-correspondence is established between (not necessarily symmetric) Tannakian categories and transitive quantum groupoids. When the base field \(k\) is perfect, a quantum groupoid over \(\text{Spec} (B)\) is transitive precisely when it is projective and faithfully flat over \(B \bigotimes_ kB\). Moreover, the fibre functor of the corresponding Tannakian category is unique up to quantum isomorphisms. Reviewer: F.Borceux (Louvain-La-Neuve) Cited in 1 ReviewCited in 17 Documents MSC: 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 20G15 Linear algebraic groups over arbitrary fields 17B37 Quantum groups (quantized enveloping algebras) and related deformations Keywords:Tannakian categories; quantum groupoids PDF BibTeX XML Cite \textit{A. Bruguières}, Commun. Algebra 22, No. 14, 5817--5860 (1994; Zbl 0808.18005) Full Text: DOI OpenURL