Related papers: On generalized near-group fusion categories

We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for…

We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized…

We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

We give a classification of Z/2Z-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples is considered.

We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules,…

We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…

In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…

We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the…

We provide a general formula for Mueger's centralizer of any fusion subcategory of a braided fusion category containing a tannakian subcategory. This entails a description for Mueger's centralizer of all fusion subcategories of a group…

Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class…

We prove that any fusion category over $\mathbb{C}$ with exactly one non-invertible simple object is spherical. Furthermore, we classify all such categories that come equipped with a braiding.

The fibre bundles adjoint to generalized almost quaternionic structures are studied. The most important classes of generalized almost quaternionic manifolds are considered.

This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety…

In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…

The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…

We introduce the concept of generalized almost plastic structure, and, on a pseudo-Riemannian manifold endowed with two $(1,1)$-tensor fields satisfying some compatibility conditions, we construct a family of generalized almost plastic…

We introduce and study the notion of slightly trivial extensions of a fusion category which can be viewed as the first level of complexity of extensions. We also provide two examples of slightly trivial extensions which arise from rank $3$…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

In this paper, we extend the notion of modular functor and fusion category to what we called $G$ equivariant modular functor and $G$ equivariant fusion category, where $G$ is a finite group, and establish a correspondence between between…