• Corpus ID: 1488726

The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

@article{Spivak2013TheOO,
  title={The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits},
  author={David I. Spivak},
  journal={ArXiv},
  year={2013},
  volume={abs/1305.0297}
}
Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the algebra $\Rel$ of mathematical relations on $\mcT$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play… 

Figures from this paper

The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes

TLDR
This work investigates the hierarchical structure of processes using the mathematical theory of operads, and defines an operad of black boxes and directed wiring diagrams of processes (which it is called propagators, after Radul and Sussman), which are useful for modeling dynamic flows of information.

Operads of Wiring Diagrams

This monograph is a comprehensive study of the combinatorial structure of various operads of wiring diagrams and undirected wiring diagrams. Our first main objective is to prove a finite presentation

The algebra of open and interconnected systems

TLDR
This thesis develops the theory of hypergraph categories and introduces the tools of decorated cospans and corelations, a more powerful version that permits construction of all hyper graph categories and hypergraph functors.

Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams

TLDR
This paper uses the language of operads to study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones, and defines two W-algebras, G and L, which associate semantic content to the structures in W.

Compositional Modeling with Stock and Flow Diagrams

TLDR
A new package called StockFlow is created, part of the AlgebraicJulia ecosystem, which uses ideas from category theory to overcome notable limitations of existing software, for building and simulating stock andow diagrams.

Hypergraph Categories

Additive monotones for resource theories of parallel-combinable processes with discarding

TLDR
The existence of complete families of additive monotones for various partitioned process theories based on the category of finite sets are shown in order to shed light on the way such families can be constructed.

C T ] 1 8 Ja n 20 19 Hypergraph Categories

Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the

Operadic Modeling of Dynamical Systems: Mathematics and Computation

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional

Structured Decompositions: Structural and Algorithmic Compositionality

TLDR
This work proves an algorithmic meta theorem for theSubP -COMPOSITION problem which, when instantiated in the category of graphs, yields compositional algorithms for NP-hard problems such as: MAXIMUM BIPARTITE SUBGRAPH, MAXIMum PLANAR SUB GRAPH and LONGEST PATH.
...

References

SHOWING 1-10 OF 28 REFERENCES

The Art of the Propagator

TLDR
A programming model built on the idea that the basic computational elements are autonomous machines interconnected by shared cells through which they communicate that makes it easy to smoothly combine expressionoriented and constraint-based programming.

Simplicial Databases

TLDR
A category DB is defined, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps, and it is proved that limits and colimits always exist in DB and that they correspond to queries such as select, join, union, etc.

Foundations of Databases

TLDR
This book discusses Languages, Computability, and Complexity, and the Relational Model, which aims to clarify the role of Semantic Data Models in the development of Query Language Design.

Table manipulation in simplicial databases

TLDR
A category of databases is developed in which the schema of a database is represented as a simplicial set, each simplex corresponds to a table in the database.

Higher Operads, Higher Categories

Part I. Background: 1. Classical categorical structures 2. Classical operads and multicategories 3. Notions of monoidal category Part II. Operads. 4. Generalized operads and multicategories: basics

The geometry of iterated loop spaces

Operads and -spaces.- Operads and monads.- A? and E? operads.- The little cubes operads .- Iterated loop spaces and the .- The approximation theorem.- Cofibrations and quasi-fibrations.- The smash

Basic category theory for computer scientists

  • B. Pierce
  • Education, Medicine
    Foundations of computing
  • 1991
TLDR
It's important for you to start having that hobby that will lead you to join in better concept of life and reading will be a positive activity to do every time.

Category theory for computing science

Preliminaries. Categories. Functors. Diagrams. Naturality and Sketches. Products and Sums. Catesian Closed Categories. Finite Discrete Sketches. Limits and Colimits. More About Sketches. Fibrations.

A Consilience-Based Approach to Engineering Services in Global Supply Chains

TLDR
A number of existing approaches to systems engineering are discussed and concluded that they are inadequate and a new, consilience-based approach is proposed that draws on the disciplines and practices that can inform and help resolve those inadequacies.

Higher Algebra

AbstractTHIS new “Higher Algebra” will be examined with great interest by all teachers and serious students of mathematics. A book of this type is certainly needed at the present time, and the one