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Mathematics > Algebraic Geometry

arXiv:1805.03485 (math)
[Submitted on 9 May 2018]

Title:Uniqueness of fiber functors and universal Tannakian categories

Authors:Daniel Schäppi
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Abstract:The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and implements a proof strategy which Deligne attributes to Grothendieck. Besides categorical generalities, the proof merely relies on basic properties of exterior powers and the classification of finitely generated modules over a principal ideal domain.
Using related ideas (but less elementary means) we also present an alternative characterization of Tannakian categories among the more general weakly Tannakian categories. As an application of this result we can construct from any right exact symmetric monoidal abelian category with simple unit object a universal Tannakian category associated to it.
Comments: 16 pages
Subjects: Algebraic Geometry (math.AG); Category Theory (math.CT)
MSC classes: 14A20, 18D10
Cite as: arXiv:1805.03485 [math.AG]
  (or arXiv:1805.03485v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.03485

Submission history

From: Daniel Schäppi [view email]
[v1] Wed, 9 May 2018 12:45:25 UTC (19 KB)
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