Abstract
In this paper, we firstly obtain the analogue of a Bongartz completion for functorially finite rigid subcategories in an extriangulated category and then we investigate the properties of n-cluster tilting subcategories in an extriangulated category for any positive integer n and show some equivalent characterization of them. Particularly, when the extriangulated category is 2-Calabi-Yau, we show any n-cluster tilting subcategories are in fact cluster tilting for any integer and they coincide with strongly contravariantly finite maximal n-rigid subcategories.
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