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I agree, the article does not actually present anything concrete. For me, the usefulness of category theory is in providing a simplifying and high level set of

I agree, the article does not actually present anything concrete. For me, the usefulness of category theory is in providing a simplifying and high level set of abstractions that can serve to illuminate the structural essence of a problem domain. At first, I thought it was just abstract nonsense (and this is coming from someone who has a PhD in mathematics), but after playing around with it a bit, I've started to appreciate the power of the concepts. The most interesting "application" of category theory that I've seen (as it relates to software engineering) is the connection between databases and category theory, e.g at https://johncarlosbaez.wordpress.com/2018/06/06/applied-category-theory-course-databases/ https://johncarlosbaez.wordpress.com/2018/06/06/applied-cate.... In short, relational schemas are categories, and common data migration operations can very naturally can be described in the language of category theory (functors, pullbacks etc).

twic 7y ago
> The most interesting "application" of category theory that I've seen (as it relates to software engineering) is the connection between databases and category theory So is this application productive? It's nice to be able to describe something that already exists in terms of category theory, and even nicer if those descriptions are concise and satisfying. But does that description enable anything new? Did we get any new migration operations, normal forms, etc?
- wisnesky 7y ago
  Yes, for example the dual of join (called 'sigma'), which only exists for databases in categorical normal form. There are many academic papers and an open-source project ('categorical query language') here: http://www.categoricaldata.net http://www.categoricaldata.net.
  - twic 7y ago
    Sounds interesting! I had a look, but couldn't find out what sigma does. This is not quite the same level as, say, the PostgreSQL documentation: http://www.categoricaldata.net/help/instancesigma.html http://www.categoricaldata.net/help/instancesigma.html Is there somewhere i can go for a worked example of using sigma?
    - wisnesky 7y ago
      Sure, here is an example that uses sigma to compute an equivalence relation: http://cql.conexus.ai/quotient.php http://cql.conexus.ai/quotient.php

twic 7y ago

> The most interesting "application" of category theory that I've seen (as it relates to software engineering) is the connection between databases and category theory So is this application productive? It's nice to be able to describe something that already exists in terms of category theory, and even nicer if those descriptions are concise and satisfying. But does that description enable anything new? Did we get any new migration operations, normal forms, etc?

wisnesky 7y ago
Yes, for example the dual of join (called 'sigma'), which only exists for databases in categorical normal form. There are many academic papers and an open-source project ('categorical query language') here: http://www.categoricaldata.net http://www.categoricaldata.net.
- twic 7y ago
  Sounds interesting! I had a look, but couldn't find out what sigma does. This is not quite the same level as, say, the PostgreSQL documentation: http://www.categoricaldata.net/help/instancesigma.html http://www.categoricaldata.net/help/instancesigma.html Is there somewhere i can go for a worked example of using sigma?
  - wisnesky 7y ago
    Sure, here is an example that uses sigma to compute an equivalence relation: http://cql.conexus.ai/quotient.php http://cql.conexus.ai/quotient.php