A quasi-categoryX is a simplicial set satisfying the restricted Kan conditions of Boardman and Vogt. It has an associated homotopy category . We show that X is a Kan complex iff is a groupoid. The result plays an important role in the theory of quasi-categories (in preparation). Here we make an application to the theory of initial objects in quasi-categories. We briefly discuss the notions of limits and colimits in quasi-categories.