Zappa–Szép products for partial actions of groupoids on left cancellative small categories

Abstract

We study groupoid actions on left cancellative small categories and their associated Zappa–Szép products. We show that certain left cancellative small categories with nice length functions can be seen as Zappa–Szép products. We compute the associated tight groupoids, characterizing important properties of them, like being Hausdorff, effective, and minimal. Finally, we determine amenability of the tight groupoid under mild, reasonable hypotheses.