COVERINGS, ACTIONS AND QUOTIENTS IN CAT1-GROUPOIDS

Abstract

The aim of this paper is to present the notions of actions and coverings of ${\text{cat}}^1$-groupoids and to prove the natural equivalence between their categories. 
Moreover, in this context, we characterize the quotient concept of ${\text{cat}}^1$-groupoids. Finally we extend these notions to ${\text{cat}}^n$-groupoids which are groupoid version of ${\text{cat}}^n$-groups.