Related papers: Nominal String Diagrams
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
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 PROP is a symmetric monoidal category, whose set of objects is the set of natural numbers and on objects the monoidal structure is given by the addition. An algebra over a PROP is a symmetric strict monoidal functor to the tensor category…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
A theory of $\infty$-properads is developed, extending both the Joyal-Lurie $\infty$-categories and the Cisinski-Moerdijk-Weiss $\infty$-operads. Every connected wheel-free graph generates a properad, giving rise to the graphical category…
Nominal unification calculates substitutions that make terms involving binders equal modulo alpha-equivalence. Although nominal unification can be seen as equivalent to Miller's higher-order pattern unification, it has properties, such as…
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…
We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…
In this paper we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
We define the graph minor category and prove that the category of contravariant representations of the graph minor category over a Noetherian ring is locally Noetherian. This can be regarded as a categorification of the Robertson--Seymour…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…
We introduce a symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces, and use the homology of its morphism spaces to define string operations. Precisely, for an $E_\infty$-ring spectrum $R$ and an oriented…