[pensativo]

Category theory is a formal semantics for (or alternative to, depending on one's perspective) type theory and thus functional programming. It's been widely used (for example, in Haskell, ML, Agda, Coq, Idris, etc) not only for formal foundations but to derive many "smaller" practical applications. Many of the creations from that domain have been useful in many other languages. Are you unaware of this and asking something else?

It's an extremely good fit and highly productive, to answer your question directly.

[sadar_]

I am aware of these applications. I am not aware of any "smaller" practical applications that are derived thanks to the categorical interpretation, can you give any examples?

[danharaj]

https://arxiv.org/abs/1502.05947

In this paper we describe a functorial data migration scenario about the manufacturing service capability of a distributed supply chain. The scenario is a category-theoretic analog of an OWL ontology-based semantic enrichment scenario developed at the National Institute of Standards and Technology (NIST). The scenario is presented using, and is included with, the open-source FQL tool, available for download at categoricaldata.net/fql.html.

This is part of a series of work on applying category theory to databases. The initial work was to cast database concepts into categorical concepts, this led to a clarification of various concepts such as many kinds of SQL query being instances of limits and colimits. The theory was then used to extrapolate via category theoretic concepts to develop new database manipulation concepts.

This is a general recipe for applying category theory, though there are other approaches.

[pensativo]

I don't have any papers on this hard drive but databases, grammar formalisms and generally many data structures (you might know about monads, comonads, arrows, zippers, etc.) If you start digging on hackage, you'll find many interesting data structures, many of which were derived categorically or at least algebraically (they often cite the papers that inspired their implementation.)

Obviously all the work can be done without category theory but since the mid-2000's I gather that many insights have been gained by exporing various categories and their relations.

Edit: I think one of the main benefits is efficiency. Even if one doesn't start from categorical formalisms, you can later use them to pare things down to what's absolutely necessary.