RE: Mathematics for Software Design: Functions, Categories, and Functors!
Thank you for your comment. I will work on improving sections 3+ for future editions. This post still fails to address some core categorical intuitions. So a 2.0 version is certainly coming.
...in hopes of applying to my work in information visualization
Interesting! Good luck with that!
I will post more about CT in the following months. Eventually I'll get into the area of your concern, i.e. modelling your particular concepts as categories.
For now I can only say:
You don't have to model your data structures as a Category in order to have a categorical design. If it's not a category, it's not a category, period. E.g. in Haskell you have the Category type class, but if a data structure doesn't satisfy the category axioms, then that's that.
Maybe your concept is an object within a category. E.g. an arrow. an object. A limit. Or some other categorical construct, and not a category in and of itself.
P.S. Maybe the "ologs" theory, developed by David Spivak, could serve your interests. If only for seeing categorical applications to modelling in action. It's like what people do with UML diagrams, except this one is helpful. :P
thanks for the response. The issue I found with Spivak is that he uses far too many mathematical concepts before getting to the heart of CT. For instance, you got to functors in one post, but it takes him chapters. ologs do make sense though and I like his analysis of databases as categories. Looking forward to more of your posts.