Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

2018 by Brendan Fong and David I. Spivak

Category theory is becoming a central hub for all of pure mathematics. It is unmatched in its ability to organize and layer abstractions, to find commonalities between structures of all sorts, and to facilitate communication between different mathematical communities. But it has also been branching out into science, informatics, and industry. We believe that it has the potential to be a major cohesive force in the world, building rigorous bridges between disparate worlds, both theoretical and practical. The motto at MIT is mens et manus, Latin for mind and hand. We believe that category theory—and pure math in general—has stayed in the realm of mind for too long; it is ripe to be brought to hand.
A very approachable but useful introduction to category theory. It avoids the Scylla and Charybdis of becoming incomprehensible after page 2 (as many academic texts do), and barely scratching the surface (as many popular texts do).

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There's an updated version available

There's an updated v3 of this paper available via arXiv.

On my list for a while, but I do keep hearing good things about it.


I recently was explaining to my wife how Moderna Therapeutics work on messenger RNA could be explained using some deep "system's theory" from category theory, and how I wondered if scientists were just sort of accidentally stumbling upon some principles that are well-known to computer scientists with background in compilers, lisp and/or languages.

She is a fifth year biomedical engineering PhD student.