I also found Awodey's category theory more helpful than Milewski's ramblings (though I appreciate his effort). Maybe it's because I find "applications in theory" worth learning.
If I may try to point out what's missing: it is the motivation which seems to get lost for lack of examples.
Here's a theory, called category theory, and many of us believe it can inform their designs, providing a perspective on compositionality, and a higher kind of equational/algebraic reasoning.
Where are the ideas and examples that will actually help us inform or designs and achieve a higher degree of compositionality? Where is our chance to apply algebraic reasoning to the programs we write?
So I will provide a lot of C++ examples. Granted, you’ll
have to overcome some ugly syntax, the patterns might not
stand out from the background of verbosity, and you might
be forced to do some copy and paste in lieu of higher
abstraction, but that’s just the lot of a C++ programmer.
Maybe this would work, but we don't actually see it in Bartosz's posts. As a different example, take Wadler's papers on comprehensions and monads (rendered as Kleisli categories): the motivation is very clear, we'd like to express certain programs/queries within a functional programming language, and all examples contribute to an understanding.
What should an experience programmer learn? One suitable answer seems to be the connection of lambda calculus with products and CCCs. That, though, would also need motivation for "functional programming", referential transparency. An alternative answer could be to point out the connection between topos theory and logic (or query languages).
It almost seems that when flipping to Haskell examples, Bartosz is making a leap that let's him ignore the motivation: anybody who is writing code in Haskell won't need to be convinced of referential transparency. There is simply a forest of "patterns" and category theory seems to be a systematic path through it. Maybe potential applications in physics provide a similar motivation for physicists.
... but if you don't bring the motivation yourself, you're not going to get it from reading the posts.
Thank you for the detailed comment. It was exactly what I was looking for. And I agree with you. I find it frustrating and inefficient if I'm just presented with the theory without any applications.
I also believe that to really understand and get an intuition for a concept, you need to see it applied, preferably in different contexts.
