<p>Inspired by Nakaoka’s series of investigations on the construction of abelian structure from a triangulated category with the help of cotorsion pairs, we want to know whether the “high dimension” ones, i.e., (left) <i>n</i>-cotorsion pairs, also have the same “function”. Through some special constructions, we obtain that the heart of a twin left <i>n</i>-cotorsion pair in a triangulated category is a preabelian category. Moreover, if we only consider a single left <i>n</i>-cotorsion pair, then its heart becomes an abelian category. At last, we give an application of some results of a twin left <i>n</i>-cotorsion pair on the colocalization sequence.</p>