MATEMATICKI VESNIK, cilt.76, sa.4, ss.280-287, 2024 (ESCI)
The aim of this paper is to present the notions of actions and coverings of cat1-groupoids and to prove the natural equivalence between their categories. Moreover, in this context, we characterize the quotient concept of cat1-groupoids. Finally we extend these notions to catn-groupoids which are groupoid version of catn-groups.