Abstract
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 (C,E,s) be an n-exangulated category and X be a strongly functorially finite subcategory of C. We then show that the quotient category C/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 necessary and sufficient condition for the quotient C/X to be an (n+2)-angulated category.
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