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String diagram

In mathematics, string diagrams are a formal graphical language for representing morphisms in monoidal categories, or more generally 2-cells in 2-categories. They are a prominent tool in applied category theory. When interpreted in FinVect, the monoidal category of finite-dimensional vector spaces and linear maps with the tensor product, string diagrams…

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Overview

History

Intuition

Definition

Extension to 2-categories

Examples

Hierarchy of graphical languages

Advanced semantic analysis

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Map overview Semantic statistics

String diagram

Nodes95
Edges94
Triples61
Avg. degree1.98
Density0.021053
Components1

How this topic connects Entity context

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String diagram

Top relations

related to history · 17
String diagram → André Joyal, Cartesian, Charles Sanders Peirce, Feynman, Frobenius, Gottlob Frege's Begriffsschrift, Günter Hotz, However, LaTeX, Peirce's, PGF/TikZ, Roger Penrose, Ross Street, The, They, This, While
related to External links · 8
String diagram → Archived, Media, Python, String, TheCatsters, Wikimedia Commons, Wiktionary-logo-en-v2, Youtube
related to Hierarchy of graphical languages · 8
String diagram → Braided, Compact, Dagger, Many, Penrose, Ribbon, Selinger's Survey, Symmetric
related to Combinatorial · 7
String diagram → Fix, In, Layers, One, Sigma, This, While
has application · 4
String diagram → Concurrency, DisCoCatQuantum, String, ZX-calculusNatural
related to Geometric · 4
String diagram → Gamma, Hausdorff, Such, The
related to The snake equation · 4
String diagram → Consider, FG, GF, The
related to Intuition · 2
String diagram → Starting, String
see also · 2
String diagram → Feynman, Proof

Important terminology Word statistics

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Important terminology

displaystyle diagrams string monoidal categories category one text two tensor diagram sigma gamma edges plane identity called list star dom

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
LaTeXinstance ofthe advent of typesetting software0.80text
PGF/TikZ made the publication of string diagrams more widespread.The existential graphsinstance ofthe advent of typesetting software0.80text
diagrammatic reasoning of Charles Sanders Peirce are arguably the oldest form of string diagramsinstance ofthe advent of typesetting software0.80text
they are interpreted in the monoidal category of finite setsinstance ofthe advent of typesetting software0.80text
relations with the Cartesian productinstance ofthe advent of typesetting software0.80text
String diagramhas applicationString0.60section
String diagramhas applicationConcurrency0.60section
String diagramhas applicationZX-calculusNatural0.60section
String diagramhas applicationDisCoCatQuantum0.60section
String diagramrelated to CombinatorialWhile0.60section
String diagramrelated to CombinatorialOne0.60section
String diagramrelated to CombinatorialIn0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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