Related papers: Entwining Structures in Monoidal Catrgories
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads…
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…
It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…
We put a Quillen model structure on the category of small categories enriched in simplicial $k$-modules and non-negatively graded chain complexes of $k$-modules, where $k$ is a commutative ring. The model structure is obtained by transfer…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…
We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary…
We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…
Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, the surjectivity of the canonical map implies bijectivity…
The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
An E_1 (or A-infinity) ring spectrum R has a derived category of modules D_R. An E_2 structure on R endows D_R with a monoidal product. An E_3 structure on R endows the monoidal product with a braiding. If the E_3 structure extends to an…
We consider the tube algebra of a spherical semisimple multitensor category $\mathcal{X}$, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with…
We introduce and study the category of twisted modules over a triangular differential graded bocs. We show that in this category idempotents split, that it admits a natural structure of a Frobenius category, that a twisted module is…
The injective polynomial modules for a general linear group $G$ of degree $n$ are labelled by the partitions with at most $n$ parts. Working over an algebraically closed field of characteristic $p$, we consider the question of which…
The main result of this paper is the construction of a trace and a trace pairing for endomorphisms satisfying suitable conditions in a monoidal category. This construction is a common generalization of the trace for endomorphisms of…
Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted…
In category theory circles it is well-known that the Schreier theory of group extensions can be understood in terms of the Grothendieck construction on indexed categories. However, it is seldom discussed how this relates to extensions of…
We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unified approach, leading to new proofs of old results by the…
In this mostly expository article, we consider certain homological aspects of branching laws for representations of a group restricted to its subgroups in the context of $p$-adic groups. We follow our earlier paper, ICM 2018 proceedings,…