The question is in the title. The category $\bf pSet$ of partial functions has sets as objects and $\hom(X,Y)=\{f\colon D\to Y\mid D\subseteq X\}$. Composition of arrows is composition of relations.

(why curly brackets do not appear?)

The question is in the title. The category $\bf pSet$ of partial functions has sets as objects and $\hom(X,Y)$ is the set of all triples $(X,Y,f)$ such that there exists $D\subseteq X$ and $f\colon D\to Y$. Composition of arrows is composition of relations.