A survey of graphical languages for monoidal categories

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Title: A survey of graphical languages for monoidal categories
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My Notes
--------
March 31, 2018

References
----------
(1) http://arxiv.org/abs/0908.3347
    A survey of graphical languages for monoidal categories, Peter Selinger, Dalhousie University
    Book chapter. In Bob Coecke, editor, New Structures for Physics, Lecture Notes in Physics 813:289–355, Springer, 2011.
    Abstract:
    This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams.
    It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists,
    and others who use diagrammatic reasoning.
    We have opted for a somewhat informal treatment of topological notions, and have omitted most proofs.
    Nevertheless, the exposition is sufficiently detailed to make it clear what is presently known, and to serve as a starting place for more in-depth study.
    Where possible, we provide pointers to more rigorous treatments in the literature.
    Where we include results that have only been proved in special cases, we indicate this in the form of caveats.

(2) https://www.mathstat.dal.ca/~selinger/papers.html

(3) https://www.mathstat.dal.ca/~selinger/papers/graphical-bib/
    References for the paper: A survey of graphical languages for monoidal categories
    with links

(4) https://arxiv.org/pdf/1307.0204.pdf
    CONNECTOR ALGEBRAS FOR C/E AND P/T NETS’ INTERACTIONS
    ROBERTO BRUNI, HERNAN MELGRATTI, UGO MONTANARI, AND PAWEL SOBOCINSKI
    Abstract.
    A quite flourishing research thread in the recent literature on componentbased
    systems is concerned with the algebraic properties of different classes of connectors.
    ...

(5) https://www.mathstat.dal.ca/~selinger/papers/graphical-bib/public/Penrose-applications-of-negative-dimensional-tensors.pdf
    R. Penrose. Applications of negative dimensional tensors. In D. J. A. Welsh, editor, Combinatorial Mathematics and its Applications, pages 221–244. Academic Press, New York, 1971.

(6) https://en.wikipedia.org/wiki/Einstein_notation
    In mathematics, especially in applications of linear algebra to physics,
    the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula,
    thus achieving notational brevity.
    As part of mathematics it is a notational subset of Ricci calculus;
    however, it is often used in applications in physics that do not distinguish between tangent and cotangent spaces.
    It was introduced to physics by Albert Einstein in 1916.

(7) https://en.wikipedia.org/wiki/Penrose_graphical_notation

(8) https://en.wikipedia.org/wiki/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, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.
    The associated natural isomorphisms are subject to certain coherence conditions, which ensure that all the relevant diagrams commute.
    In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the category.
    They are also used in the definition of an enriched category.

(9) https://ncatlab.org/nlab/show/monoidal+category

(10) http://math.ucr.edu/home/baez/qg-fall2004/definitions.pdf

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