  We introduce (continuous) partial category actions on sets (topological
spaces) and show that each such action admits a universal globalization.
Thereby, we obtain a simultaneous generalization of corresponding results for
groups, by Kellendonk and Lawson, and for monoids, by Megrelishvili and
Schroder. We apply this result to the special case of partial groupoid actions
where we obtain a sharpening of a result by Gilbert, concerning ordered
groupoids, in the sense that mediating functions between universal
globalizations always are injective.
