> I think it's safe to say that most mathematicians in 2016 -- let alone software engineers -- are pretty unfamiliar with category theory
I'm sure that's true for software engineers, but my experience is that category theory has permeated most fields to a significant degree. Many recent graduate-level texts on fields of mathematics from topology to differential geometry to algebra incorporate at least basic category theory like functors and natural transformations. It's even more common at the research level. And I say all of this not having actually met a single actual category theorist, only those in other fields who used at least some of it.
I'm sure that's true for software engineers, but my experience is that category theory has permeated most fields to a significant degree. Many recent graduate-level texts on fields of mathematics from topology to differential geometry to algebra incorporate at least basic category theory like functors and natural transformations. It's even more common at the research level. And I say all of this not having actually met a single actual category theorist, only those in other fields who used at least some of it.