According to this wikipedia page, a monoid is defined as an object that contains
- An associative binary operation
- An identity element
There is no mention of the object necessarily containing a set.
The same page includes the statement "a monoid is a semigroup with an identity element". It is my understanding that a semigroup is a magma with additional constraints, is this correct?
The page also compares a monoid and a magma, stating a monoid simply has more constraints. But doesn't a monoid lack magma's constraint of having to contain a set?
So does this mean a monoid does necessitate a set? Or have I misunderstood something?
I might just be nitpicking the specific wording of a wikipedia page, but I don't want to assume it's an error before I understand it for sure.
Thanks in advance!