I only know two theorems for neutral Tannaka categories. (1) One states that the set of $k$-group scheme homomorphisms $m:G_1\to G_2$ is in one to one correspondence with the set …

This is a question about the proof of proposition 1.13 in Deligne and Milne, Tannakian Categories. Let $C,C'$ be two rigid tensor categories and $F,G : C \rightarrow C'$ be two ten …

If $G$ is an affine group scheme over a field $k$, then we have the forgetful functor $\omega$ from the category ${\rm Rep}_k(G)$ of finite representations of $G$ to the category o …

Let $K$ be a field of characteristic zero, and let $G \subseteq \mathrm{GL}_V$ be an algebraic group over $K$, acting faithfully on a finite dimensional vector space $V$. Let $H \s …

Let $\mathfrak g$ be a finite-dimensional Lie algebra over $\mathbb C$, and let $\mathfrak g \text{-rep}$ be its category of finite-dimensional modules. Then $\mathfrak g\text{-re …

This question is motivated by my attempts to answer the question http://mathoverflow.net/questions/96149 from the point of view of Tannaka reconstruction. This has led me to the fo …

I've recently realized that there is a gap in my understanding of the Tannakian formalism for reconstructing an (algebraic) group from its category of (finite-dimensional) represen …

Suppose that $G$ is an algebraic group over a field $k$. Then for any $k$-algebra $R$, a fiber functor from $\text{Rep}_k(G)$ to the category of projective modules over $R$ is the …

I've read that one way to formulate the Langlands program is the following: Let $\mathcal{L}_ {\mathbb{Q}}$ be the conjectural Langlands group. Then the category of semi-simple (c …

It is well known that if I have a differentialable manifold (holomorphic maniford) $M$, then I have a functor from the categroy of vector bundles on $M$ with flat connections to th …

I will take the approach of this question: http://mathoverflow.net/questions/23860/tannaka-formalism-and-the-etale-fundamental-group and think of the etale fundamental group as Ta …

As anyone who's been reading the forums closely can see, I've been averaging a question a day about Tannakian formalism for the past few days. It's quite an interesting concept! I …

It is well-know that the category of coherent D-modules over a smooth algebraic $k$-scheme is a Tannakian category. So it is equivalent to the category of finite representations of …

This is a basic question about Grothendieck's conjectural category $M_k$ of pure motives (over a field $k$). This construction first produces a category (the "false category of mot …

If $\mathfrak{C}$ is a $k$-linear rigid abelian tensor category with End(1)=$k$(strictly speaking is isomorphic to $k$ as a $k$-algebra), and $k=\bar{k}$, and if $\omega_1$ and $\o …