Over a million developers have joined DZone.

Visualizing Category Concept Dependencies

· Java Zone

Learn more about how the Java language, tools and frameworks have been the foundation of countless enterprise systems, brought to you in partnership with Salesforce.

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.

Discover how the Force.com Web Services Connector (WSC) is a code-generation tool and runtime library for use with Force.com Web services, brought to you in partnership with Salesforce.

Topics:

Published at DZone with permission of John Cook, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}