Nrthugu

First of all, sorry, but I'm not a native English speaker. I will however try to do my best.

I'm actually studying some theoretical concepts as a hobby to deepen my understandings of functional programming and have some questions to check that I correctly understood what a monoid is.

First of all, the definition of a monoid that I found is that a monoid is a set that is closed under an associative binary operation and has an identity element. I guess it's correct?

So, using the following definition, I suppose that Scala's lists form a monoid under the ::: operator, as List is a set, ::: is associative (xs ::: (ys ::: zs) = (xs ::: ys) ::: zs) and List has a base element (Nil). Am I right?

Regarding monoids, is there something to say about the :: List operator? I suppose not as it's not taking two lists as parameters, but an element and a List. Am I still right?

First of all, the definition of a monoid that I found is that a monoid is a set that is closed under an associative binary operation and has an identity element. I guess it's correct?

As far as I know, that is correct. (disclaimer: I am still learning too).

So, using the following definition, I suppose that Scala's lists form a monoid under the ::: operator, as List is a set, ::: is associative (xs ::: (ys ::: zs) = (xs ::: ys) ::: zs) and List has a base element (Nil). Am I right?

Also correct.

For example here is the definition of Monoid[List[A]] in Cats - and here is an specification of the Monoid[List[A]] in Scalaz.

Both are libraries/frameworks for functional programming in scala, and as you can see they both define the Monoid for List using ::: and Nil.

Regarding monoids, is there something to say about the :: List operator? I suppose not as it's not taking two lists as parameters, but an element and a List. Am I still right?

Again as far as I know, you're still right.