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!

$Y^X$ is a common notation for functions $f:X\to Y$. The notation with "Fun" in it is often used for functors (so where $X$ and $Y$ are categories). The notation with "Map" in it I have mostly encountered in topology for continuous functions $X\to Y$ (so where $X$ and $Y$ are topological spaces). Don't take this too strict though. — drhab, Jan 18 '18 at 16:08

score 4 · Accepted Answer · answered Jan 18 '18 at 16:08

4

Set theorists simply call it $Y^X$.

answered Jan 18 '18 at 16:08

Nate Eldredge

score 3 · Answer 2 · answered Jan 18 '18 at 18:47

3

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

answered Jan 18 '18 at 18:47

Luca Bressan

3

Oftentimes the name of the category is used without the "Hom", e.g. $\mathbf{Set}(X,Y)$. This is a bit less typographically overwhelming. – Derek Elkins left SE Jan 18 '18 at 22:02

2 Answers2