Related papers: Reasoning with !-Graphs
Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to…
Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…
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,…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
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…
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…
!-graphs provide a means of reasoning about infinite families of string diagrams and have proven useful in manipulation of (co)algebraic structures like Hopf algebras, Frobenius algebras, and compositions thereof. However, they have…
This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
Categorical quantum mechanics (CQM) and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques.…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
In work of Fokkinga and Meertens a calculational approach to category theory is developed. The scheme has many merits, but sacrifices useful type information in the move to an equational style of reasoning. By contrast, traditional proofs…
The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…
A popular graphical calculus for monoidal categories makes computations tactile and intuitive. Complicated diagram chases can be expressed in a few pictures and discovered by playing with a shoelace. Joyal and Street's proof of the…
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we…
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…
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…