Related papers: Monoidal centres and groupoid-graded categories

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

As shown in a previous paper by the same authors, the theory of Galois functors provides a categorical framework for the characterisation of bimonads on any category as Hopf monads and also for the characterisation of opmonoidal monads on…

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…

The notion of the center of an algebra over a field k has a far reaching generalization to algebras in monoidal categories. The center then lives in the monoidal center of the original category. This generalization plays an important role…

Monoidal functors U:C --> M with left adjoints determine, in a universal way, monoids T in the category of oplax monoidal endofunctors on M. Such monads will be called bimonads. Treating bimonads as abstract "quantum groupoids" we derive…

This is a first of a series of two papers. Our motive is to tackle the question raised in B\"ohm's "The Gray Monoidal Product of Double Categories" from Applied Categorical Structures: which would be an alternative notion to intercategories…

In this paper using split extensions of group-groupoids we obtain the notion of crossed modules over group-grouoids which are also called 2-groups and we prove a categorical equivalence of these types of crossed modules and double…

We study the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence…

Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…

Let $G$ be a finite group and $G'$ its commutator subgroup. By a sequence over $G$, we mean a finite unordered sequence of terms from $G$, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered…

We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.

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…

We define the monoidal category $(Poly_E,y,\triangleleft)$ of polynomials under composition in any category $E$ with finite limits, including both cartesian and vertical morphisms of polynomials, and generalize to this setting the Dirichlet…

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

Let $\mathcal{S}$ be a small category admitting binary products. We show that the whole theory of monoidal $\mathcal{S}$-fibered categories, which is customarily formulated in terms of the usual internal tensor product, can be rephrased…

Univalent categories constitute a well-behaved and useful notion of category in univalent foundations. The notion of univalence has subsequently been generalized to bicategories and other structures in (higher) category theory. Here, we…

For a smooth affine algebraic group $G$, one can attach various D-module categories to it that admit convolution monoidal structure. We consider the derived category of D-modules on $G$, the stack $G/G_{ad}$ and the category of…

Let $\mathcal{C}$ be a finite braided multitensor category. Let $B$ be Majid's automorphism braided group of $\mathcal{C}$, then $B$ is a cocommutative Hopf algebra in $\mathcal{C}$. We show that the center of $\mathcal{C}$ is isomorphic to…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

We define the notion of the $(G,\Gamma)$-crossed center of a $(G,\Gamma)$-crossed tensor category in the sense of Natale. We show that the $(G, \Gamma)$-crossed center is a $(G \bowtie \Gamma, G \times \Gamma)$-braided tensor category. This…