michael_nielsen

are you familiar with “An Invitation to Category Theory for Designers”? it tries to explicitly make the connection between abstraction in the context of design (esp architecture) & category theory as a toolset for dealing with abstraction in general http://mathematicians.org.uk/eoh/files/CTFD8.pdf …

No, I haven’t. Must admit, I took a class on category theory, and didn’t get a lot out of it (almost the only math class of which that was true; certainly the only well-taught class of which that was true).

The better "designed" a mathematical system is in this way the harder it is to make progress with unsolved mathematical problems though. Most beautiful axiomatic systems are very rigid and optimised to make you see exactly what the authors want you to see.

Group theory is a great example of this. The conventional axioms focus entirely on the algebra. But really there are many things about groups that are more easily seen if one thinks of the group elements as permutations (which is what they always are).