> Have you tried thinking up new mathematical objects? Yes, I have. Off the top of my head, the objects I'm interested in are often monoidal, but usually lack

> Have you tried thinking up new mathematical objects? Yes, I have. Off the top of my head, the objects I'm interested in are often monoidal, but usually lack inverses. Strings don't have any natural group structure (though as free monoids there is an obvious way to extend them into free groups), nor metric spaces or context-free grammars or finite state machines. Of course groups are ubiquitous, but I think your claims of universality are vastly exaggerated.