A Note On Simplicial Groupoids

Abstract

Showing the equivalence of the two categories is very important interms of investigating the properties. This equivalence shows that theproperties existing in the category exist in the other category without theneed to examination. From this point of view, since the category of groupoidsis a category better known than the category of simplicial groupoids, thanksto equivalence, all the properties in the category of groupoids are valid forthe category of simplicial groupoids. Main objective of this paper is to givesimplicial object in category of groupoids and to prove the equivalencebetween the category of simplicial groupoids and the category of crossedmodules of groupoids.