Functional Programming and Category Theory
These colleagues of yours, would they happen to be Haskell aficionados?
They might have told you that Hask was a category made from Haskell, but that is a lie, notheless a very useful one that inspires new programming techniques.
If you would like to find out how category theory informs functional programming, I can recommend Bartosz Milewski's Category theory for programmers.
There is also the older Category theory for computer science by Michael Barr and Charless Wells, which is more of a straight introduction to category theory. It might be a good book for functional programmers who only ever learned the bastardized category theory through functional programming.