# Can pointed sets category have an arrow that points to the same set?

In the category of pointed sets [p.17, Awodey], can there be an arrow that points to the same set but with a different distinguishing element?

I.e., if I have a set $A=\{1,2,3\}$, can there an arrow $f: (A,1) \to (A,2)$?

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A constant map $f = 2$ for example. –  Makoto Kato Oct 28 '12 at 5:08
Sure. Any set function $f:A \to A$ with $f(1)=2$ gives such an arrow.