All Questions

Filter by
Sorted by
Tagged with
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 $Y$ ...
Meths's user avatar
  • 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 ...
Dmitri Pavlov's user avatar
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 $k$-...
Vanessa's user avatar
  • 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 ...
Manuel Bärenz's user avatar
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 $\otimes_{H}$ ?
lun's user avatar
  • 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 ...
Manuel Bärenz's user avatar