All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor.
So we have the category $X$ with Endofunctor $T: X \rightarrow X $
And two natural transformations: $$\eta: 1_X \rightarrow T $$ $$ \mu: T^2 \rightarrow T $$
Question: Since $T$ is the object of this Monoid, what are its elements? I understand that the elements are:
$$ \forall x \in X: T(x), T^2(x), T^3(x),...,T^n(x),...$$
Is that correct?
This is a followup to Monoid in the category of endofunctors and Monoid as a category with one object