You wouldn't. I think saying you used category theory to design something just sounds cool and is basically a shibboleth. In fact, any time you compose functions you're using category theory. I think it sounds a little pretentious to be honest. No one says they used boolean logic when they wrote some code so saying you used category theory or type theory sounds equally weird.

I work with a guy that has a PhD in some heavy duty categorical machinery and I haven't heard him once say he used category theory to design some piece of code.