**String diagram ** String diagram. Jump to navigation Jump to search. In category theory, string diagrams are a way of representing morphisms in monoidal categories, or more generally 2 cells in 2 categories.

**[1401.7220] Category Theory Using String Diagrams arXiv** By contrast, traditional proofs by diagram pasting retain the vital type information, but poorly express the reasoning and development of categorical proofs. In order to combine the strengths of these two perspectives, we propose the use of string diagrams, common folklore in the category theory community, allowing us to retain the type ...

**string diagram in nLab** Overview 0.1. String diagrams are a graphical calculus for expressing operations in a monoidal category. The idea is roughly to think of objects in a monoidal category as “strings” and a morphism from one tensor product to another as a node which the source strings enter and the target strings exit.

**Category theory and diagrammatic reasoning 4 String ...** Category theory and diagrammatic reasoning 20th February 2019 Last updated: 19th February 2019 4 String diagrams and algebraic theories String diagrams are an alternative representation for 2 cells and their compositions in a bicategory. A 2 cell with two 1 cells in its source and one 1 cell in its target has the

**category theory Good reference for string diagrams ...** $\begingroup$ there are no string diagrams in Borceux. I think he just meant it is the best overall text on category theory in general. The Catsters on youtube have a couple videos on string diagrams. $\endgroup$ – Rachmaninoff Dec 2 '15 at 22:39

**What is a string diagram? Quora** Concisely: A string diagram is the Poincaré dual for the manifold with corners underlying a diagram in a 2 category. Verbosely: String diagrams give us topological geometric interpretations for higher algebraic relations inside of 2 categories. In a classical diagram, we have objects (points, 0 dimensional),...

**ct.category theory The two ways Feynman diagrams appear ...** The two ways Feynman diagrams appear in mathematics. They can be seen as "string diagrams" describing various type of arrows (and or compositions operations on them) in a monoidal closed category. They are combinatorial tools that allow one to give formulas for the asymptotic expansion of integrals of the form: when in terms...

**QPL2017 Dan Marsden. String diagrams for category theory** QPL2017 Dan Marsden. String diagrams for category theory ... Homotopy Type Theory: What's the Big Idea #YOWLambdaJam ... A Pragmatic Introduction to Category Theory—Daniela Sfregola ...

**What is a string diagram, and what is the purpose of a ...** A string diagram is a useful aid for following purposes: (1) It represents the record of an existing set of conditions and thus helps the method engineer in visualizing the actual situation. (2) It indicates complex movements, back tracking, congestion, bottle necks and over and underutilized paths on the shop floor.

**Category theory ** Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

**DanMarsden November11,2014 arXiv:1401.7220v2 [math.CT] 9 ...** By contrast, traditional proofs by diagram pasting re tain the vital type information, but poorly express the reasoning and development of categorical proofs. In order to combine the strengths of these two perspectives, we propose the use of string diagrams, common folklore in the category theory community, allowing us to retain the type

**diagram in nLab** Every category C C admits a unique diagram whose shape is the empty category, which is called the empty diagram in C C. The shape of the terminal diagram is the terminal category J = { * } J = \{*\} consisting of a single object and a single morphism (the identity morphism on that object).

**The Catsters Strike Again: "String Diagrams" | The n ...** The Catsters Strike Again: “String Diagrams” Posted by John Baez You may have thought the Catsters was a funny stage name for Eugenia Cheng… but now the other Catster, Simon Willerton, steps in front of the camera and demonstrates his star power: The Catsters, 5 lectures on String diagrams.; This guy is full of energy.

**Maths Category Theory Monad Martin Baker** Monad using String Diagrams. more about string diagrams on this page. Because there is only one object, it is not shown on the string diagram. So, in this case, crossing over the line means going once round the endofunctor 'T'. ... Category theory deals with links (functions, morphisms and so on) between a range of mathematical structures like ...

**String Diagrams** 3 13 String Diagrams for Free Monads Duration: ... Category Theory: Adjoint Functors Part 1 Duration: ... String Theory Explained – What is The True Nature of Reality? ...

**Category theory what's the intuition behind diagrams ...** I'm new to category theory, and I'm trying to understand diagrams. What's the connection between the pencil and paper diagrams that I draw in my workbook, and the technical definition that a diagram is a functor? Does every pencil and paper diagram I can draw give rise to a unique diagram in the technical sense, in a unique way?

**Hottest 'string diagrams' Answers MathOverflow** Hot answers tagged string diagrams. day week month year all. ... the search is for a calculation of the asymptotic expansion of Gaussian integrals using concepts and techniques from category theory. Here is one such calculation: Feynman diagrams via graphical calculus (2001) There is a very close connection between the graphical formalism for ...

**strid – A string diagrams generator smimram.github.io** strid – A string diagrams generator. strid is a tool to generate string diagrams for inclusion in LaTeX documents. These diagrams are often used in category theory as a convenient way to represent 2 cells in 2 categories. It has a syntax which is inspired of Xy matrix (but dual diagrams

**Category Theory Using String Diagrams ResearchGate** String diagrams provide category theory with a different and very distinctive visual flavour. We demonstrate that they are an effective tool for equational reasoning using a variety of examples ...

**XY pic tutorial with an archive of examples** Markov moves archive and embedding eps files in xypic diagrams Cobordisms. Cobordism tutorial with many example . String diagrams. String diagram tutorial with many examples. Diagrams from category theory. commutative diagrams; globular 2 cells; globular 3 cells. Diagrams from topology. algebraic topology and Morse theory . Miscellaneous ...

**Maths Category Theory Adjunction Martin Baker** Category Diagram String Diagram ; We start with a diagram like this (F is left adjoint to G) and add 2 natural transformations below (η and ξ) with the following axioms. We take this diagram: between functors and put it in a diagram with the objects. The string diagram has the identity functor omitted as explained above.

**Categories and String Diagrams | SkillsCast | 6th October 2016** This talk introduces string diagrams as a notation for calculating in category theory. You will learn the diagrams to better understand monads, adjunctions, and finally free monads. All of this, of course, is relevant to the curious Haskell programmer who wants to better understand abstract nonsense.

**The Yoneda lemma and String diagrams SlideShare** The Yoneda lemma and string diagrams When we study the categorical theory, to check the commutativity is a routine work. Using a string diagrammatic notation, the commutativity is replaced by more intuitive gadgets, the elevator rules.

**String diagrams for game theory ResearchGate** String diagrams are useful tools in many disciplines, including physics, computer science and linguistics. Their language is closely related to category theory.

**String diagram Revolvy** String diagram topic. In category theory , string diagrams are a way of representing 2 cells in 2 categories . Definition The idea is to represent structures of dimension d by structures of dimension 2 d, using the Poincaré duality .

**Applied Category Theory Course Azimuth Forum** Talk to people with similar interests in the Applied Category Theory course! ... Lecture 73 Chapter 4: String Diagrams and Strictification. Category Applied Category Theory Course 0 points Started by John Baez ments 24 Last comment by Christopher Upshaw Last active 07 Sep 2018.

**Category:Category theory Wikimedia mons** Media in category "Category theory" The following 159 files are in this category, out of 159 total. 2 Morphisms Between 2 Categories of FRBSU Monoidal Categories and Crossed Modules.pdf 1,275 × 1,650, 76 pages; 495 KB

**11 Fig 13 The String Interaction diagram when consider ...** Fig 1.3. – The String Interaction diagram when consider higher order terms in perturbation theory The nice thing about this is that at each order in perturbation theory there is only one diagram. [For a comparison, in point particle field theories the number of diagrams grows exponentially at higher orders.] The problem lies in the fact that to extract answers from diagrams with more than ...

**Conditional Reasoning with String Diagrams sa logic.org** Conditional Reasoning with String Diagrams 403 2 Category theory, string diagrams and deductive sys tems String diagrams can be used in physics (e.g., [3]) and computer science (e.g., [23]) to

**Physics, Topology, Logic and putation: A Rosetta Stone** Physics, Topology, Logic and putation: A Rosetta Stone John C. Baez ... Category theory is a very general formalism, but there is a certain special way that physicists use categories ... String theory exploits this analogy by replacing the Feynman diagrams of ordinary quantum eld theory with 2 dimensional cobordisms, which represent the ...

**Basic Category Theory (OPLSS 2016) Wesleyan University** Category theory can be thought of as a sort of generalized set theory, where the primitive concepts are those of set and function, rather than set and member ship. This shift of perspective allows categories to more directly describe many structures, even those that are not particularly set like. In category theory, the

**QG Seminar: Fall 2006 University of California, Riverside** Quantum Gravity Seminar Fall 2006 John Baez and Derek Wise ... Classical versus quantum lambda calculus. From lambda terms to string diagrams. Internalizing composition. The "untyped" lambda calculus. Church numerals and booleans. ... Lambda calculus and category theory. Peter Selinger, Lecture notes on the lambda calculus.

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