The purpose of this text is the study of the class of homotopy types which are modelized by strict $\infty$-groupoids. We show that the homotopy category of simply connected strict $\infty$-groupoids is equivalent to the derived category in homological degree $d \ge 2$ of abelian groups. We deduce that the simply connected homotopy types modelized by strict $\infty$-groupoids are precisely the products of Eilenberg-Mac Lane spaces. We also briefly study 3-categories with weak inverses. We finish by two questions about the problem suggested by the title of this text.
Keywords: strict $\infty$-groupoid, homotopy type, chain complex, homotopy category, Eilenberg-Mac Lane space
2010 MSC: 18B40, 18D05, 18E30, 18E35, 18G35, 18G55, 55P10, 55P15, 55Q05, 55U15, 55U25, 55U35
Theory and Applications of Categories, Vol. 28, 2013, No. 19, pp 552-576.