A monoid is a category, a category is a monad, a monad is a monoid

I work at Target and we have a weekly class on algebra, category theory and Haskell because people are interested. It's a mix of programmers learning some of the math and mathematicians learning some of the programming :).

It's actually a lot more accessible than it seems at first—these ideas are not complex, just abstract. Thinking at a high level of abstraction is very much a skill which requires specific training, but it's a skill worth training and, when you have it, learning things like this becomes much easier.

The same thing is true of programming, by the way: once you start "thinking like a programmer", it becomes much easier to learn a new programming language or to understand some low-level programming concepts. And thinking like a programmer is, in the grand scale of things, not that different from thinking like a mathematician!

That sounds awesome!

Is Haskell (or other fp languages) commonly used at Target?

I'm slowly developing a systematic framework for programming the human brain with foundations in category theory. I've gotten a lot of useful mileage out of what little I've learned about category theory. It contributes to my intuition about how to reprogram my brain. I'm convinced we'll be teaching it to children in the future, once the programming framework is better developed and understood.

What could be more practical than self-improvement?

I'll answer my own question: learning how to apply the same kinds of reasoning to improve how people interact.

I've been studying Leibniz recently and I'm excited to get to his treatment of Monads. The following is a little irrelevant to this post, but the title of this post stirred a relationship.

So to Leibniz, in the conception of an entity's identity, he posits that one must include all propositions related to that entity. So when we try to consider a property of an object of our mind, we are basically saying "it is what it is." Saying that Einstein is German is like saying "Einstein is Einstein." Where this conception of including propositions in identities gets weird is that his formulation also includes future propositions. In this respect, only God can truly understand anything fully, because only he can tell the future and can get the full identity of things.

So "x is x" shows up a lot.

Edit: As mentioned, Leibniz Monad != the Monad of category theory. I suppose I'm just looking for any excuse to talk about Leibniz. Also, I did say I didn't even get to that topic yet. Consider this a peep about the duality of that term.

I guess I'll raise my hand by commenting.

This stuff is a certain brand of abstract algebra. Abstract algebra is generally of a certain degree of usefulness to a programmer in that there's a similarity in discipline. Moreover, linear algebra can be very useful to many programers who do things related to applied mathematics---nearly all of it touches linear algebra. Linear algebra is a specific form of abstract algebra and this blog takes a particularly "abstract" approach to linear algebra.

The particular tools being used here are of a category theoretic flavor. Category theory is a sibling to abstract algebra especially popular in certain fields (topology, algebraic geometry, foundations and logic). It's furthermore pretty popular in the Haskell-like FP crowd since Haskell is a rich place for exploring very high-order abstraction and category theory helps provide some language for talking at very high abstraction. For that reason, a lot of Haskell hackers have some amount of experience with category theory.

Finally, hackers with any kind of pure math background have a decent chance at having been exposed to this stuff. Even if they weren't, there's a good chance they could read it with some fluency. Math is a lot like programming where once you get your water legs you have a significantly improved time digesting related subjects even without direct prior experience.

For myself I have a bit of a math background, was drawn to Haskell for that reason, discovered category theory via Haskell, then swung full circle and read about it as a branch of pure math to learn more about foundations and logic.