Category Theory for the Working Hacker [video]

Then from what I'm understanding it's not an "arrow", it's something closer to a "step" or a "process". Some method to get from one location to another. An arrow means nothing without background information. If I say it takes "10 arrows to get from A to x(A)" as a way to explain there are 10 things happening in the function X, then wouldn't it be better to say it takes "10 steps/processes to get from A to x(A)"?

> The name comes from that kind of representation.

The representation, the way I conceive it, is a mode for displaying computational or data in a spacial manor. As such relating a computational or mathematical process to a spacial terminology would be a "step" not a stick with a rock at the end of it.

Does step help when thinking of the objects as individual data elements, the arrows as cons-links, map being a functor that respects cons-links [i.e. does not change the structure of the list]? The problem here is that implying process, ordering, or anything else is too narrow of a definition for what an arrow/morphism can be used to represent. That's why arrow (a thing that points to another thing), or morphism (a thing that helps define the shape) are actually better terms. Because Category Theory isn't about the things, it's about the relationships between the things, how these can be composed, and how higher-order operators that respect these relationships [and the new ones they represent for even higher-order operators] can form new relationships which can also be composed.

As a working programmer that is curious about category theory, I feel like this misses the mark completely. I watched this yesterday, and this is what I remember:

1) I will tell you why category theory is relevant to you, the working programmer.

2) Here are the 2 most important data structures that you don't use in your day job.

3) Look at how they relate in this mathy not applicable way.

4) Conclusion: lambda calculus is awesome.

What I would like to see is:

1) I will tell you why category theory is relevant to you, the working programmer.

2) Here is a realistic but simplified problem and a solution written in python that is obviously the wrong approach to solving the problem. With category theory, we know this is the wrong approach because the math is wrong (and don't go into the math).

3) Here is another example that seems like a decent approach to solving the problem. With category theory, we know this is the wrong approach because the math is wrong (and don't go into the math). Doing it our way has these benefits...

4) Conclusion: learn category theory to become a better programmer.

If you can't do that, find some other way to illustrate the concrete benefits of learning category theory. If there aren't any concrete benefits, it's like telling baseball players they should learn physics to have a better understanding of baseball.