Related papers: The Condensed Fiber Product and Zesting
This paper presents some basic facts about the so-called connectivity spaces. In particular, it studies the generation of connectivity structures, the existence of limits and colimits in the main categories of connectivity spaces, the…
Structured and decorated cospans are broadly applicable frameworks for building bicategories or double categories of open systems. We streamline and generalize these frameworks using central concepts of double category theory. We show that,…
We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some…
We define a local version of the extended symplectic category, the cotangent microbundle category, MiC, which turns out to be a true monoidal category. We show that a monoid in this category induces a Poisson manifold together with the…
We introduce web supercategories of type Q. We describe the structure of these categories and show they have a symmetric braiding. The main result of the paper shows these diagrammatically defined monoidal supercategories provide…
We construct a monoidal version of Lurie's un/straightening equivalence. In more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow the $\infty$-category of coCartesian fibrations over $\mathbf C$ with a (naturally…
The reduced universal monoid on the action category associated to a pointed simplicial M-set has appeared in the guise of various simplicial monoid and group constructions. These include the classical constructions of Milnor and James, as…
It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that…
We classify braided $\mathbb{Z}_q$-extensions of pointed fusion categories, where $q$ is a prime number. As an application, we classify modular categories of Frobenius-Perron dimension $q^3$.
This paper is devoted to further results on the nontrivially associated categories $\mathcal{C}$ and $\mathcal{D}$, which are constructed from a choice of coset representatives for a subgroup of a finite group. We look at the construction…
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…
By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor…
This work is a detailed version of arXiv:0704.0195 [math.QA]. We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also…
We compare three different ways of defining group cohomology with coefficients in a crossed-module: 1) explicit approach via cocycles; 2) geometric approach via gerbes; 3) group theoretic approach via butterflies. We discuss the case where…
We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the…
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for…
Braided monoidal categories arise naturally as centres of monoidal categories and have been the focus of much recent attention in both mathematics and physics. By suitably restricting the use of the exchange rule, we obtain a sequent…
An example of double cross coproducts with both non-trivial left coaction and non-trivial right coaction in strictly braided tensor categories is given.
Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev invariants. The deformation theory of braidings is…
We describe all fusion subcategories of the representation category of a twisted quantum double of a finite group. In view of the fact that every group-theoretical braided fusion category can be embedded into a representation category of a…