What is a common notation for set of functions from X to Y?

Question

Is there a common notation for the set of functions from a set $X$ to a set $Y$?

Is $\text{Fun}(X,Y)$ commonly used? (I recall seeing it somewhere.)

How about $\text{Map}(X,Y)$?

I am aware that there are some usages in category theory for the above two notations, I hope to find one notation that does not cause confusion.

Thanks!

Answer 1

Set theorists simply call it $Y^X$.

Answer 2

If you are already dealing with categories and you want your notation to be consistent, you might just use $\mathrm{Hom}_{\mathrm{Set}}(X, Y)$.