Map/Reduce as an Example of Programming...

Category Theory is normally considered conceptually, inspiring data structures, but it also has a computational side (viz. monads). The question then comes, can one consider categories as a programming language and what would that look like? Deferring the general question, this will show a reduction of the Map/Reduce programming paradigm to categories using a lot of basic categorical machinery, such as monoids, free monoids, functors and fibres and then show how the resulting, fully functional, program, implemented in Scala, can be further reduced to execute on multiple platforms, such as Hadoop and Spark. This will provide a practical view of categories for the working non-mathematician and should be at least amusing, if not enlightening.