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.

Keywords: $\text{Cat}^n$-groupoid; covering; action; normality; quotient.

MSC: 20L05, 18D35, 18B40, 20M50

DOI: 10.57016/MV-SPDF3739

Pages:  1$-$8