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I'm a PhD student in category theory, more specifically I study 2-dimensional category theory, that means bicategories, pseudofunctors, careful definitions of various structures you can put on this stuff and possible application to the representation theory of finite group(oid)s. I'm enthusiastic about this formalism, but at the same time I'm not sure yet whether research may fit my life interest for many other reasons.

I wouldn't like to abbandon category theory once my PhD will be over, and as far as I know one of the main subjects "outside accademia" that may require a solid background in category theory is functional programming, of which I barely know some general features differentiating it from more imperative type of programming, but really, I don't know much about programming at all.

So, my question is: could you provide some references in order to approach a self learning of functional programming with an eye on categorical aspects? More generally, based on what just said, are there other areas that you feel like suggesting that I find out about?

Thank you so much in advance :)

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The blog by Bartosz Milewski comes to my mind. It focusses on the interplay between Haskell and category theory.

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Besides the CT-functional programming connection, in recent years a field of "applied category theory" (ACT) has emerged that seeks to apply category-theoretic ideas to fields beyond the traditional ones of mathematics, logic, and programming language theory. It is hard to summarize this program in a few words, but some themes that seem important to me are:

  • The use of symmetric monoidal categories and wiring diagrams/string diagrams to model processes, both physical or computational (see the Rosetta Stone paper)
  • Studying open systems (systems with an interface/boundary) and their composition, trying to put old ideas about "systems science" or "general systems theory" on a firm mathematical foundation
  • Extending the scope of functorial semantics, originally introduced by Lawvere, from models of logical theories to models in science, engineering, and statistics
  • Creating a new mathematics of relational databases, knowledge representation, and data integration based on category theory

To get a sense of what people in ACT are doing, you might peruse the papers published in the new journal Compositionality or at the ACT conference.

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  • $\begingroup$ @MartinBrandenburg Followed immediately by "More generally, based on what just said, are there other areas that you feel like suggesting that I find out about?", and with a question title about 'domains that may require a categorical background'. $\endgroup$
    – Steven Stadnicki
    Commented Nov 23, 2022 at 17:59

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