All Questions
6
questions
8
votes
1
answer
279
views
R-matrices and symmetric fusion categories
Given a $\mathbb{C}$-linear braided fusion category $\mathcal{C}$ containing a fusion rule of the form e.g.
\begin{equation}X\otimes Y\cong A\oplus B \oplus C\end{equation}
(where $A,B, C, X$ and $Y$ ...
- 277
7
votes
3
answers
585
views
Does one of the hexagon identities imply the other one?
Suppose we have a monoidal category equipped with additional data that almost makes it a braided monoidal category except that only one of the hexagon identities
is satisfied.
Can we then prove the ...
- 35.6k
6
votes
2
answers
758
views
Module categories over symmetric/braided monoidal categories
Given an algebraically closed field $k$ and a finitely generated commutative $k$-algebra $A$, all simple modules over $A$ are 1-dimensional
What is the analogous statement for symmetric monoidal $k$-...
- 1,358
5
votes
2
answers
1k
views
When is the endofunctor category of a monoidal category braided? When is it ribbon? Fusion? Modular?
Given a category $\mathcal{C}$, we can define the category of endofunctors $\operatorname{Cat}(\mathcal{C})$, with objects functors $F: \mathcal{C} \to \mathcal{C}$ and morphisms natural ...
- 5,485
5
votes
1
answer
446
views
Braided monoidal category, example
Let $H$ be a cocommutative hopf algebra.
Let $M$ be the category of $H$-bimodules.
Does the category $M$ form a braided monoidal category with tensor product $\otimes_{H}$ ?
- 69
2
votes
1
answer
141
views
How nontrivial can "central extensions of ribbon fusion categories" be?
In a sense, this is a follow up on this question, but one PhD programme later.
Let $\mathcal{C}$ be ribbon fusion. By $\mathcal{C}'$, we denote the symmetric centre, i.e. the full subcategory of ...
- 5,485