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John Cook is an applied mathematician working in Houston, Texas. His career has been a blend of research, software development, consulting, and management. John is a DZone MVB and is not an employee of DZone and has posted 171 posts at DZone. You can read more from them at their website. View Full User Profile

Visualizing Category Concept Dependencies

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Category theory has a high ratio of definitions to theorems, and it can seem like every definition depends on an infinite regress of definitions. But if you graph the definition dependencies, the graph is wide rather than deep.

I picked out 65 concepts and created a visualization using GraphViz. No definition is more than six degrees away from first principles, and most are closer. The graph is four to five times wider than it is tall, too wide to include here, so here’s a section from the middle:

The full graph is available here.

It’s possible to define concepts in different ways and obtain a different graph. I used definitions from here.

Here is a list of other math diagrams I’ve created.

Published at DZone with permission of John Cook, author and DZone MVB. (source)

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