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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 \mathcal{T} over a base field k is a rigid abelian tensor category with an k-linear exact faithful tensor \omega: \mathcal{T}  \longrightarrow \textrm{Vect}_k (\rm{Vect}_k being the category of vector spaces over k) which one calls the fiber functor.

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