Related papers: Braided Near-group Categories
We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
A relative category is a category with a chosen class of weak equivalences. Barwick and Kan produced a model structure on the category of all relative categories, which is Quillen equivalent to the Joyal model structure on simplicial sets…
In this paper, we generalizing the main result in Liu[10] to weak Hopf coquasigroups case. We first define and study group-cograded weak Hopf quasigroups, which generalize both group-cograded Hopf quasigroups and weak Hopf group-coalgebras.…
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided…
We define pseudo-Garside groups and prove a theorem about them parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. We introduce a group B=B(Z^n)…
We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…
We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and…
Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there…
We show several geometric and algebraic aspects of a necklace: a link composed with a core circle and a series of circles linked to this core. We first prove that the fundamental group of the configuration space of necklaces (that we will…
In this article we describe indecomposable objects of the derived categories of a branch class of associative algebras. To this class belong such known classes of algebras as gentle algebras, skew-gentle algebras and certain degenerations…
For a quasitriangular C*-quantum group, we enrich the twisted tensor product constructed in the first part of this series to a monoidal structure on the category of its continuous coactions on C*-algebras. We define braided C*-quantum…
We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group $\Omega \mathsf{O}(n)$ on each $\mathcal{E}_{n-1}$-monoidal $(g,d)$-category $\mathcal{R}$ in which…
Thick simplices are the nerves of the contractible groupoids obtained by inverting the arrows in the categories [n]. Using explicit expansions of simplicial subsets of the thick simplices, we present a new approach to results of Rezk and of…
We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which…
We classify the module categories over the double (possibly twisted) of a finite group.
In this paper we present a unified proof of the fact that the category of modules over a ring and the category of near-vector spaces in the sense of J. Andr\'e, over an appropriate scalar system (a 'scalar group'), are both abelian…
We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed…
In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…
In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the connection between the self-distributivity law LD and braids…