Improving "Given a type A, all endomorphisms defined on A are a monoid" sentence?

[SHND]

Instead of sentence:

Given a type A, all endomorphisms defined on A are a monoid

isn't it more correct to say:

Given a type A, all endomorphisms defined on A under function composition operation are a monoid

Because semigroups are defined on pair of type A and operation on type A.

[enricopolanski]

@SHND I think this is correct.

You've got:

• a type A

• a function A => A, our endomorphism

• the identity function as the empty element

Maybe a better phrasing would be:

"Given a type A, all endomorphims defined on A form (define?) a monoid.