http://www.cs.ox.ac.uk/people/bob.coecke/AbrNikos.pdf
Why study categories—what are they good for? We can offer a range of answers for readers coming from different backgrounds:
- For mathematicians: category theory organises your previous mathematical experience in a new and powerful way, revealing new connections and structure, and allows you to “think bigger thoughts”.
- For computer scientists: category theory gives a precise handle on important notions such as compositionality, abstraction, representationindependence, genericity and more. Otherwise put, it provides the fundamental mathematical structures underpinning many key programming concepts.
- For logicians: category theory gives a syntax-independent view of the fundamental structures of logic, and opens up new kinds of models and interpretations.
- For philosophers: category theory opens up a fresh approach to structuralist foundations of mathematics and science; and an alternative to the traditional focus on set theory
- For physicists: category theory offers new ways of formulating physical theories in a structural form. There have inter alia been some striking recent applications to quantum information and computation.
https://www.cs.ox.ac.uk/files/3395/PRG72.pdf