[Math] Real world applications of category theory

Question

I was reading some basic information from Wiki about category theory and honestly speaking I have a very weak knowledge about it. As it sounds interesting, I will go into the theory to learn more if it is actually useful in practice.

My question is to know if category theory has some applications in practice, namely in engineering problems.

I have already read this Applications of category theory and topoi/topos theory in reality

and the answers are only about programming which are not very interesting from my point of view.

Any comments are welcomed, thanks in advance.

Answer 1

The blog entry "Why Category Theory Matters" by Robert Seaton ends with a quite impressive reference list of applications of category theory to the sciences:

• Category theory has been used to study grammar and human language.
• In building a spreadsheet application.
• As a descriptive tool in neuroscience.
• In the analysis and design of cognitive neural network architectures.
• In programming languages, especially Haskell and most famously monads, but also, for instance, a typed assembly language and work on the typed lambda calculus.
• Generating program optimizations.
• To model systems of interacting agents.
• To generalize sorting algorithms.
• To understand collaborative text editing. See also this blog.
• To understand optimal play in sequential games like chess.
• To formalize the notion of algorithm.
• In the study of analogy.
• As “a language for experimental design patterns” and “a new vocabulary in which to think and communicate.”
• In definitions of emergence and discussions of biology.