In this talk we discuss locally constant cocycles taking values in the special linear group. Such a cocycle is uniformly hyperbolic if the norms of matrix products in the image of the cocycle grow exponentially with respect to the length of the product. Using techniques from the theory of Möbius semigroups, we study the locus of all uniformly hyperbolic cocycles which was introduced by Avila, Bochi and Yoccoz. Our goal is to answer a question posed by these three authors and modified by Jacques and Short.