Abstract Given an extriangulated category (C, E, s) (C, E, s), we introduce the (3 3) (3 × 3) -lemma property for subfunctors of E E and prove that an additive subfunctor F F of E E is closed if, and only if, it satisfies this condition. This characterization extends a well known result by A. Buan (for abelian categories) to extriangulated categories. As an application of this result, we get a new equivalent condition to describe saturated proper classes ξ in C C.
Cala et al. (2026) studied this question.
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