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Of late, a lot of people have been asking me about Tannakian categories, so I decided to post this short blurb (mainly to check the Latex-related features of wordpress and also to provide some bird’s-eye view of why we should care about Tannakian categories.)

To begin with:

**Definition**

A *neutral Tannakian category * over a base field is a rigid abelian tensor category with an -linear exact faithful tensor* * ( being the category of vector spaces over ) which one calls the *fiber functor*.

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