How do you recover a group from the automorphisms of the forgetful functor?

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The discussion focuses on recovering a group from the automorphisms of the forgetful functor in the context of neutral Tannakian categories. It establishes a bijection between the category of representations of a group and the automorphisms of the forgetful functor that maps these representations to their corresponding vector spaces. The participants emphasize the importance of understanding this relationship to illustrate the recovery process, referencing theoretical resources and examples for further clarity.

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  • Neutral Tannakian categories
  • Forgetful functors in category theory
  • Group representations
  • Understanding of automorphisms in mathematical structures
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Jim Kata
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Ok, I doubt anyone on here will know this, but given a neutral tannakain category there is a bijection between this category and the representations of some group (with some adjectives). I'm not sure how to show that, don't care though. But, to recover the group from the category of representations you look at the automorphisms of the forgetful functor from the category of representations of the the group to the vector space created by the representations of the group. How exactly do you recover the group from the automorphisms of the forgetful functor? Illustrate this with an example.
 
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