Théorie tannakienne non commutative
作者:
Alain Bruguières,
期刊:
Communications in Algebra
(Taylor Available online 1994)
卷期:
Volume 22,
issue 14
页码: 5817-5860
ISSN:0092-7872
年代: 1994
DOI:10.1080/00927879408825165
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
Inspired by a recent paper by Deligne [2], we extend the Tannaka-Krein duility results (over a field) to the non-commutative situation. To be precise, we establish a 1-1 corresponde:ice between ‘tensorial autonomous categories’ equipped with a ‘fibre functor’ (i. e. tannakian categories without the commutativity condition on the tensor product), and ‘quantum groupoids’ (as defined by Maltsiniotis, [9]) which are ‘transitive’ (7.1.). When the base field is perfect, a quantum groupoid over SpecBis transitive iff it is projective and faithfully fiat overB⊗kB. Moreover, the fibre functor is unique up to ‘quantum isomorphism’ (7.6.). Actually, we show Tannaka-Krein duality results in the more general setting where there is no monoidal structure on the category (and the functor); the algebraic object corresponding to such a category is a ‘semi-transitive’ coalgebroid (5.2. and 5.8.).
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