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).

An enjoyable 25-minute introductory talk: YOW! Lambda Jam 2019 - Ken Scambler - Applied Category Theory (slides)

What do programming, quantum physics, chemistry, neuroscience, systems biology, natural language parsing, causality, network theory, game theory, dynamical systems and database theory have in common?

As functional programmers, we know how useful category theory can be for our work - or perhaps how abstruse and distant it can seem. What is less well known is that applying category theory to the real world is an exciting field of study that has really taken off in just the last few years. It turns out that we share something big with other fields and industries - we want to make big things out of little things without everything going to hell! The key is compositionality, the central idea of category theory.

Previously: Seven Sketches in Compositionality: An Invitation to Applied Category Theory.

(via Brian McKenna)

Once thought too abstract, category theory has become remarkably pervasive in science, says mathematician and pianist Eugenia Cheng