I see monoids more and more everyday. A bit outside the topic but does anyone have a good introduction-level resource to learning monoids?
Think for example about learning about the "iterator" abstraction. It's just something with "hasNext" and "next" operations, nothing more to understand. But when you know it you start seeing iterators everywhere, and you get frustrated when something that should be an iterator isn't so you cannot write a simple foreach loop. And you'll start implementing iterators in your own code, because you know that provides a lot of convenience for free to consumers.
Same thing for monoids. They're everywhere, they offer some convenience for free, and you'll be wondering why things that should have monoid instances don't.
Julie Moronuki's blog has helped me greatly to understand it all: https://argumatronic.com/posts/2019-06-21-algebra-cheatsheet...
I am not good with Haskell but I meant in general mathematical / algebraic introduction, explanation or a lecture.
I've had some luck with the first chapter of this (free) [2] book, although they explain groups and not monoids but for me it was then rather quick to gain intuition about monoids.
[1] https://en.wikipedia.org/wiki/Monoid#Relation_to_category_th...
https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
In any case, doesn't adding more properties make a theory simpler? For example the classification of finite simple groups is much harder than the classification of finite simple commutative groups.
(It's not focused on Monoids. It also covers groups, rings, and fields from a mathematical point of view. It's written for an undergraduate math major with no prior experience in these areas.)