# The algebra of open and interconnected systems

@article{Fong2016TheAO, title={The algebra of open and interconnected systems}, author={Brendan Fong}, journal={arXiv: Category Theory}, year={2016} }

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, Petri nets, chemical reaction networks, and so on. The key feature is that the language is comprised of a number of components with multiple (input/output) terminals, each possibly labelled with some type, that may then be connected together along…

## 62 Citations

### Picturing resources in concurrency

- Computer Science
- 2018

It is shown to axiomatise a category of open Petri nets, in the style of the connector algebras of nets with boundaries first studied by Bruni, Melgratti, Montanari and Sobociński.

### A recipe for black box functors

- Computer Science
- 2018

It is argued that the category of decorating data is a good setting in which to construct any hypergraph functor, giving a new construction of Baez and Pollard's black box functor for reaction networks as an example.

### A Universal Construction for (Co)Relations

- Computer ScienceCALCO
- 2017

It is shown how semantic categories of both relations and corelations can be characterised as colimits of simpler categories, which simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams.

### Rewriting with Frobenius

- Computer ScienceLICS
- 2018

A DPO rewriting formalism which is able to absorb multiple Frobenius structures, thus sensibly simplifying diagrammatic reasoning in the analysis of compound systems in a compositional, resource-sensitive manner.

### 1 0 D ec 2 01 8 A recipe for black box functors

- Computer Science
- 2018

It is argued that the category of decorating data is a good setting in which to construct any hypergraph functor, giving a new construction of Baez and Pollard’s black box functor for reaction networks as an example.

### A Compositional Framework for Reaction Networks

- Mathematics, Computer Science
- 2017

This work constructs a "black-boxing" functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states, which extends earlier work on black-boxing for Markov processes.

### Universal Constructions for (Co)Relations: categories, monoidal categories, and props

- Computer ScienceLog. Methods Comput. Sci.
- 2018

This paper shows how semantic categories of both relations and corelations can be characterised as colimits of simpler categories, which simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams.

### Props in Network Theory

- Computer Science
- 2017

A new proof of the black-boxing theorem proved by Fong and the first author is given and a morphism of props is used to clarify the relation between circuit diagrams and the signal-flow diagrams in control theory.

### A Compositional Framework for Passive Linear Networks

- Mathematics
- 2015

Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where…

### Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective

- Mathematics
- 2018

Author(s): Coya, Brandon Hector | Advisor(s): Baez, John | Abstract: We use the framework of ``props" to study electrical circuits, signal-flow diagrams, and bond graphs. A prop is a strict symmetric…

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