5 ms·
This was posted several times recently without anyone noting that it was the origin of "A monad is a monoid in the category of endofunctors, what's the problem?
by gnufx 5y ago
This was posted several times recently without anyone noting that it was the origin of "A monad is a monoid in the category of endofunctors, what's the problem?", which often seems to be quoted as if it wasn't attributed to Wadler satirically.
- patrickthebold 5y agoWithout the 'what's the problem', It's in 'categories for the working mathematician' by Saunders Mac Lane. Of course, it's entirely seriously in that book.
- karatinversion 5y agoAnd a perfectly fine turn of phrase in that context, too.
- LambdaComplex 5y agoAnd burritos are just tacoids in the category of enchiladafunctors. https://twitter.com/rickasaurus/status/705134684427128833 https://twitter.com/rickasaurus/status/705134684427128833
- benrbray 5y agoFor anyone looking for an explanation, this StackOverflow question [1] is worth a read. [1] https://stackoverflow.com/questions/3870088/a-monad-is-just-a-monoid-in-the-category-of-endofunctors-whats-the-problem https://stackoverflow.com/questions/3870088/a-monad-is-just-...
- siraben 5y agoThe funny part is that it's completely true, albeit not very useful if one doesn't know how monoid constructions work categorically (good explanation at [0]). Algebra: Chapter 0 has a similar overly technical definition for groups (which they elaborate of course). Also see[1] Joke 1.1. Definition: A group is a groupoid with a single object. [0] https://old.reddit.com/r/math/comments/ap25mr/a_monad_is_a_monoid_in_the_category_of/ https://old.reddit.com/r/math/comments/ap25mr/a_monad_is_a_m... [1] https://i.pinimg.com/originals/e3/b6/23/e3b62382a9eb1021ff3086184c7ca05a.png https://i.pinimg.com/originals/e3/b6/23/e3b62382a9eb1021ff30...
- AzzieElbab 5y agoIt means monad is a thing that sequentially combines computations on the same type. Of course there is more to it but i believe this definition is useful as a starting point
- gnufx 5y agoI don't think anyone doubts the technical fact, or it wouldn't be a decent joke. The problem is if people think Wadler (might have) said it as such, and that it reflects a community attitude. It's trotted out often enough in a disparaging way. As far as I remember, Milewski left it to the end as something he just felt obliged to show.