Abstract

In this paper, we study the pullbacks of [Formula: see text]s (respectively, [Formula: see text]-[Formula: see text]s). We also study the homological properties of [Formula: see text]s (respectively, [Formula: see text]-[Formula: see text]s). More specifically, it is proved that the only possible weak global dimensions (respectively, [Formula: see text]-weak global dimensions) of an [Formula: see text] (respectively, a [Formula: see text]-[Formula: see text]) are [Formula: see text] and [Formula: see text].

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