All Questions
Tagged with braided-tensor-categories tannakian-category
5
questions
11
votes
1
answer
694
views
Is the category $\operatorname{sVect}$ an "algebraic closure" of $\operatorname{Vect}$?
$\DeclareMathOperator\sVect{sVect}\DeclareMathOperator\Vect{Vect}$The category $\sVect_k$ of (let's say finite-dimensional) super vector spaces can be obtained from the category $\Vect_k$ of (finite-...
- 59k
11
votes
0
answers
650
views
What is the role of fiber functor in Deligne's theorem on Tannakian categories?
The theorem states that, for a field $k$ of characteristic 0, any $k$-linear tensor category with $End(1)=k$ satisfying a condition that each object is annihilated by a Schur functor, is equivalent to ...
- 223
9
votes
3
answers
723
views
Generalized Tannakian Duality?
By the classical theory of Tannakian duality we know that every $k$-linear rigid abelian tensor category ($k$ a field) which has a fibre functor to $\mathrm{Vec}_k$ (finite dim. vector spaces over $k$)...
- 4,454
5
votes
1
answer
235
views
Tannakian reconstruction for braided categories
Let $\mathcal{C}$ be a symmetric monoidal category. One can imagine a theorem
Tannakian reconstruction: If $\mathcal{B}$ is a braided monoidal category and $F:\mathcal{B}\to \mathcal{C}$ is a functor ...
- 5,278
4
votes
1
answer
474
views
Faithful exact functors to tensor categories
Let $P$ be a "nice" $k$-linear abelian tensor category (e.g. A tannakian category or a fusion category over a field $k$) and $F: M\to P $ an additive $k$-linear exact and faithful functor. I want to ...
- 4,454