I am a mathematician and generally bearish on category theory in programming. The best argument for it I've seen so far is that it can inform the design of your system to give it desirable properties, like how the DVCS Pijul [1] bases its data structures on patches and its merge operation on categorical pushouts [2] -- also explained at length in a series of blog posts [3]. I found the whole idea and reasoning behing the merge system very convincing, and am not sure it could have been arrived at or explained as clearly without category theory guiding the way.

[1] https://pijul.org/ [2] https://arxiv.org/abs/1311.3903 [3] https://jneem.github.io/merging/