### Burritos for Category Theorists

#### Posted by John Baez

You’ve probably heard of Lawvere’s Hegelian taco. Now here is a paper that introduces the *burrito* to category theorists:

- Ed Morehouse, Burritos for the hungry mathematician.

The source of its versatility and popularity is revealed:

To wit, a burrito is just a strong monad in the symmetric monoidal category of food.

Frankly, having seen plenty of attempts to explain monads to computer scientists, I thought this should have been marketed as ‘monads for chefs’. But Mike Stay, who pointed me to this article, explained its subtext:

Haskell uses monads all over the place, and programmers who are not used to functional programming often find them confusing. This is a quote from a widely-shared article on the proliferation of “monad tutorials”:

After struggling to understand them for a week, looking at examples, writing code, reading things other people have written, he finally has an “aha!” moment: everything is suddenly clear, and Joe Understands Monads! What has really happened, of course, is that Joe’s brain has fit all the details together into a higher-level abstraction, a metaphor which Joe can use to get an intuitive grasp of monads; let us suppose that Joe’s metaphor is that Monads are Like Burritos. Here is where Joe badly misinterprets his own thought process: “Of course!” Joe thinks. “It’s all so simple now. The key to understanding monads is that they are Like Burritos. If only I had thought of this before!” The problem, of course, is that if Joe HAD thought of this before, it wouldn’t have helped: the week of struggling through details was a necessary and integral part of forming Joe’s Burrito intuition, not a sad consequence of his failure to hit upon the idea sooner.

The article is this:

- Brent Yorgey, Abstraction, intuition, and the “monad tutorial fallacy”, January 12, 2009.

## Re: Burritos for Category Theorists

Have you seen this elaboration of the ‘monads are like burritos’ idea?