Quasi-categories and Kan complexes

A quasi-categoryX is a simplicial set satisfying the restricted Kan conditions of Boardman and Vogt. It has an associated homotopy category ho X. We show that X is a Kan complex iffho X 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.