From 7869f6b4aa660c07913dddd1def3fc69256aa69b Mon Sep 17 00:00:00 2001 From: jim Date: Thu, 19 Mar 2015 14:21:02 -0400 Subject: [PATCH] add links to category theory --- topics/week7_introducing_monads.mdwn | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/topics/week7_introducing_monads.mdwn b/topics/week7_introducing_monads.mdwn index 84fdace5..33bdc979 100644 --- a/topics/week7_introducing_monads.mdwn +++ b/topics/week7_introducing_monads.mdwn @@ -12,7 +12,15 @@ can be unhelpful. There's a backlash about the metaphors that tells people to instead just look at the formal definition. We'll give that to you below, but it's sometimes sloganized as [A monad is just a monoid in the category of endofunctors, what's the problem?](http://stackoverflow.com/questions/3870088). -Without some intuitive guidance, this can also be unhelpful. We'll try to find a good balance. +Without some intuitive guidance, this can also be unhelpful. We'll try to find a good balance. + +(After you've read this once and are coming back to re-read it to try to digest the details further, the "endofunctors" that slogan is talking about are the boxing operations. Their "monoidal" character is captured in the Monad Laws, where a "monoid"---don't confuse with a mon*ad*---is a simpler algebraic notion, meaning a universe with some associative operation that has an identity. For advanced study, here are some further links on the relation between monads as we're working with them and monads as they appear in category theory: +[1](http://en.wikipedia.org/wiki/Outline_of_category_theory) +[2](http://lambda1.jimpryor.net/advanced_topics/monads_in_category_theory/) +[3](http://en.wikibooks.org/wiki/Haskell/Category_theory) +[4](https://wiki.haskell.org/Category_theory), where you should follow the further links discussing Functors, Natural Transformations, and Monads.) + + The closest we will come to metaphorical talk is to suggest that monadic types place values inside of *boxes*, and that monads wrap -- 2.11.0