You are currently browsing the category archive for the ‘motives’ category.

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.