Related papers: Webs of Type P
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…
Webs are combinatorial diagrams used to encode homomorphisms between representations of Lie (super)algebras and related objects. This paper extends the theory of webs to the quantum group of type Q. We define a monoidal supercategory of…
Let $\mathbb{k}$ be a characteristic zero domain. For a locally unital $\mathbb{k}$-superalgebra $A$ with distinguished idempotents $I$and even subalgebra $a \subseteq A_{\bar 0}$, we define and study an associated diagrammatic monoidal…
We introduce a new diagrammatic $\Bbbk$-linear monoidal supercategory $QWeb^\bullet$, the affine web supercategory of type $Q$, where $\Bbbk$ is a commutative ring of characteristic not two. This category is the affinization of the web…
In the literature, one finds several competing notions for the super (i.e., Z/2-graded) analog of a monoidal category. The goal of this paper is to clarify these definitions and the connections between them. We also discuss in detail the…
We extend the Schur algebra and the polynomial web category of the symmetric group to the hyperoctahedral group. In particular, we define the hyperoctahedral web category diagrammatically by generators and relations, and prove that it is…
Let $\mathbb{k}$ be a characteristic zero domain. We define and study a diagrammatic monoidal $\mathbb{k}$-linear supercategory $\mathbf{Web}^{aff}_{A}$ associated to any locally unital Frobenius $\mathbb{k}$-superalgebra $A$. This category…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We introduce two families of diagrammatic monoidal supercategories. The first family, depending on an associative superalgebra, generalizes the oriented Brauer category. The second, depending on an involutive superalgebra, generalizes the…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
We give a natural-deduction-style type theory for symmetric monoidal categories whose judgmental structure directly represents morphisms with tensor products in their codomain as well as their domain. The syntax is inspired by Sweedler…
We define a $\mathbb{C}(q)$-linear pivotal category $\mathbf{Web}(\mathfrak{sp}_{2n})$ and prove that it is equivalent to the full subcategory of finite-dimensional representations of $U_q(\mathfrak{sp}_{2n})$ tensor-generated by the…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
Generalizing the polynomial web category, we introduce a diagrammatic $\Bbbk$-linear monoidal category, the affine web category, for any commutative ring $\Bbbk$. Integral bases consisting of elementary diagrams are obtained for the affine…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We give a generators and relations presentation for the full monoidal subcategory of representations of the quantum orthogonal group generated by the quantum exterior powers of the defining representation.
We define web categories describing intertwiners for the orthogonal and symplectic Lie algebras, and, in the quantized setup, for certain orthogonal and symplectic coideal subalgebras. They generalize the Brauer category, and allow us to…
The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with…
This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the…