Related papers: Dynamic Tracing: a graphical language for rewritin…
A Sequential Dynamical System (SDS) is a quadruple (\Gamma, S_i,f_i,w) consisting of a (directed) graph \Gamma=(V,E), each of whose vertices i\in V is endowed with a finite set state S_i and an update function f_i: \prod_{j, i \to j} S_j…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal…
We construct a strict pivotal monoidal category $\mathcal{D}_{\mathrm{DNA}}$ whose objects are DNA sequences (words over $\{A,C,G,T\}$) and whose morphisms are isotopy classes of typed noncrossing planar matchings, composed of…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
The familiar trace of a square matrix generalizes to a trace of an endomorphism of a dualizable object in a symmetric monoidal category. To extend these ideas to other settings, such as modules over non-commutative rings, the trace can be…
A coalgebraic definition of finite and infinite trace semantics for probabilistic transition systems has recently been given using a certain Kleisli category. In this paper this semantics is developed using a coalgebraic method which is an…
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…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
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…
Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the last decades. They can be thought of as symmetric monoidal…
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
Within the Geometry of Interaction (GoI) paradigm, we present a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the…
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…
Execution of concurrent programs implies frequent switching between different thread contexts. This property perplexes analyzing and reasoning about concurrent programs. Trace simplification is a technique that aims at alleviating this…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the…
We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database…