Abstract
In the past recent years, I have been using string diagrams to teach basic category theory (adjunctions, Kan extensions, but also limits and Yoneda embedding). Using graphical notations is undoubtedly joyful, and brings us close to other graphical syntaxes of circuits, interaction nets, etc... It saves us from laborious verifications of naturality, which is built-in in string diagrams. On the other hand, the language of string diagrams is more demanding in terms of typing: one may need to introduce explicit coercions for equalities of functors, or for distinguishing a morphism from a point in the corresponding internal homset. So that in some sense, string diagrams look more like a language ”à la Church”, while the usual mathematics of, say, Mac Lane’s ”Categories for the working mathematician” are more ”à la Curry”.
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References
Curien, P.-L.: Category theory: a programming language-oriented introduction (forthcoming)
Kassel, C.: Quantum groups. Springer, Heidelberg (1995)
Mac Lane, S.: Categories for the working mathematician. Springer, Heidelberg (1971)
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© 2008 Springer-Verlag Berlin Heidelberg
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Curien, PL. (2008). The Joy of String Diagrams. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_2
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DOI: https://doi.org/10.1007/978-3-540-87531-4_2
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