Category of pointed sets
= Category of pointed sets
{title2=$\mathbf{Set}_*$}
The category of <pointed sets> and basepoint-preserving <functions> is a <pointed category>. It is equivalent to the <category of partial functions> by adjoining or deleting the basepoint. It is not isomorphic to the category of all actual sets and partial functions: there are many distinct singleton <zero objects>, whereas the empty set is the sole zero object in that category.