Actions and Partial Actions of Inductive Constellations

Abstract. Inductive constellations are one-sided analogues of inductive categories which correspond to left restriction semigroups in a manner analogous to the correspondence between inverse semigroups and inductive groupoids. In this paper, we define the notions of the action and partial action of an inductive constellation on a set, before introducing the Szendrei expansion of an inductive constellation, which is modelled closely on that defined by Gilbert (2005) for inductive groupoids. The main result of the paper is a theorem which uses this Szendrei expansion to link the actions and partial actions of inductive constellations, and is analogous to results previously proved by various authors for groups, monoids, and other objects.