In this article, we introduce the notion of a pre-(n + 2)-angulated category as a higher dimensional analogue of a pre-triangulated category defined by Beligiannis-Reiten. We first show that the idempotent completion of a pre-(n + 2)-angulated category admits a unique pre-(n + 2)-angulated structure. Let (if,E,s) be an n-exangulated category and X be a strongly functorially finite subcategory of if. We then show that the quotient category if/X is a pre-(n + 2)-angulated category. These results allow to construct several examples of pre-(n + 2)-angulated categories. Moreover, we also give a nec...
