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

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Does $\bf pSet$ admit products?

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?)