相关论文: Monoidal functor categories and graphic Fourier tr…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
We introduce and investigate new invariants on the pair of modules $M$ and $N$ over quantum affine algebras $U_q'(\mathfrak{g})$ by analyzing their associated R-matrices. From new invariants, we provide a criterion for a monoidal category…
In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and…
Kato has constructed reflection functors for KLR algebras which categorify the braid group action on a quantum group by algebra automorphisms. We prove that these reflection functors are monoidal.
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer-Kan equivalences, i.e. enriched functors…
In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…
We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of…
In this document, we collect a list of categorical structures on the category $\mathbf{Poly}$ of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but…
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
Whereas formal category theory is classically considered within a $2$-category, in this paper a double-dimensional approach is taken. More precisely we develop such theory within the setting of augmented virtual double categories, a notion…