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-Sz´ep products. We show that certain left cancellative small categories with nice length functions can be seen as Zappa-Sz´ep 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.