[Cladode]

But why is that a problem?

Category theory is an API for mathematics that was developed with specific applications in mind that the API seeks to unify and make easier to think about. Those application domains are algebraic geometry, algebraic topology, homological/homotopical algebra. Every API comes with trade-offs: typically an API makes one domain easier, at the cost of making other domains harder. Example: CSS is Turing complete. And I think CSS is really good at helping with styling webpages. But I would not want to write a compiler is CSS.

Computer scientists, like myself, who read from Page 150 onwards have just found the API stylised for algebraic geometry, algebraic topology, homological/homotopical algebra, ... not that useful, for applications in computer science. Unlike the first 50 pages, which have been very useful. More specifically, we found the cost of using purely categorical APIs not worth the benefits in many application domains. Maybe we are missing something, maybe we overlooked something. But, given the investments since the 1990s of computer science into category theory, I'd like to see more evidence for!

To conclude with a concrete example: why would I write a compiler using an API for homotopical algebra?