= Category of partial functions
{title2=$\mathbf{Part}$}
The category $\mathbf{Part}$ has <sets> as objects and <partial functions> as morphisms. Composition is defined where both successive functions are defined. The nowhere-defined map is a <zero morphism>, and the empty set is its sole actual <zero object>. Adjoining a tagged basepoint turns a partial function into a total basepoint-preserving function, giving an <equivalence of categories> with the <category of pointed sets>.
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