> category theory is completely detached from reality One could very easily object to that, computable structure theory sounds very concrete indeed. But even

> category theory is completely detached from reality One could very easily object to that, computable structure theory sounds very concrete indeed. But even taking that statement at face value, you are not really disproving that math is a tool. It is a tool for describing formal thinking. For example, a forgetful functor from Grp to Set is the formalization of the idea that you may take the underlying set from a group "forgetting" about the algebraic structure. There is value in having language and tools to describe that kind of thinking, even if it is very abstract. The choice of which mathematical objects to study is basically arbitrary. This is not to say that math is useless, quite the opposite. It's probably the most consequential human invention after writing, but I'm very skeptical of trying to assign metaphysical meanings to it.