I'll use the following code for answer your questions:
idd : (A : Set) → A → A
idd A a = a
idd a polymorphic function? No. Agda (without universe polymorphism) is a monomorphic language. The
idd function is only defined on small types, i.e.
Set. The function is not defined on
idd a dependent type? Yes. I'll quote Bove and Dybjer [2009, p. 64]:
Here we see a first use of dependent types: the type
A -> A depends on the
A : Set ranging over the small types.
Bove, A. and Dybjer, P. (2009). Dependent Types at Work. In: LerNet ALFA Summer School 2008. Ed. by Bove, A., Soares Barbosa, L., Pardo, A. and Sousa Pinto, J. Vol. 5520. Lecture Notes in Computer Science. Springer, pp. 57–99.