Category Relationships in Mathematical Physics

The diagram below is a computer-generated version of a hand-drawn diagram in Robert Geroch’s book Mathematical Physics. The original diagram is better in some ways because Geroch arranges the classes in a way that implies structure not captured by the arrows. Solid arrows represent forgetful functors, i.e. there is a solid line from A to B if you can make every A into a B by ignoring some structure. Dashed lines indicate a free construction.

Here is the GraphViz file used to create the diagram.

Topological Spaces, Sets, Complete Uniform Spaces, Uniform Spaces, Complete Topological Groups, Topological Groups, Groups, Complete Abelian Topological Groups, Abelian Topological Groups, Abelian Groups, Complete Real Topological Vector Spaces, Real Topological Vector Spaces, Real Vector Spaces, Real Lie Algebras, Real Associative Algebras, Complete Complex Topological Vector Spaces, Complex Topological Vector Spaces, Complex Vector Spaces, Complex Lie Algebras, Complex Associative Algebras


More mathematical diagrams