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Everything about String diagram
Graphical representation of a morphism
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 are called tensor networks or Penrose graphical notation. This has led to the development of categorical quantum mechanics where the axioms of quantum theory are expressed in the language of monoidal categories. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: String diagramA 5-minute orientation
- Skim a recent paper: String diagram rewrite theory III: Confluence with and without FrobeniusInfluential work since 2022
- Pick up a classic book: Instrumental handbookThe most-reprinted book on the subject
- Read the landmark paper: Moving heavy quarkonium entropy, effective string tension, and the QCD phase diagramCited 41 times
- Go sideways: Monoidal functorA closely related topic
- Go sideways: Premonoidal categoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Moving heavy quarkonium entropy, effective string tension, and the QCD phase diagram
A group theoretic method for string loop diagram
Mixed traffic flow of human-driven vehicles and connected autonomous vehicles: String stability and fundamental diagram
Poisson equation for the Mercedes diagram in string theory at genus one
Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states
String Diagram Rewrite Theory I: Rewriting with Frobenius Structure
Poisson equation for the three-loop ladder diagram in string theory at genus one
String diagram rewrite theory II: Rewriting with symmetric monoidal structure
🆕 Influential since 2022
String diagram rewrite theory III: Confluence with and without Frobenius
The torus one-point diagram in two-dimensional string cosmology
Bifurcation Diagram and Dynamic Response of a Drill String Applied in NGH Drilling
SUCKER RODS STRING DESIGN – RODS FATIGUE BEHAVIOR INTERPRETATION USING GOODMAN DIAGRAM
Collages of String Diagrams
📚 Books worth reading
- 📕Instrumental handbookRobert S. Smith · 1951
- 📕Chords and tuning for fretted instrumentsLarry Sandberg · 1977
How to write songs on guitarRikky Rooksby · 2000
The Ultimate Guitar Chord Big BookDon Latarski, Aaron Stang · 1998- 📕Audels New Electric Library Vol. VII; For Engineers, Electricians, All Electrical Workers, Mechanics, And StudentsFrank D. Graham · 1946
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Monoidal category In mathematics, a monoidal category (or tensor category) is a category 𝐂 equipped with a bifunctor ⊗:𝐂×𝐂→𝐂 that is associative up to a natural isomorphism…
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- Pasting theorem In higher category theory in mathematics, the pasting theorem guarantees that each pasting diagram has a uniquely defined composite that independent of…
- Multiplicative graph In mathematics, a multiplicative graph (in French: graphe multiplicatif or neocategory in some English-language papers) is an algebraic structure in category…