Given an extriangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$, we
introduce the $3 \times 3$-lemma property for subfunctors of $\mathbb{E}$ Und
prove that an additive subfunctor $\mathbb{F}$ of $\mathbb{E}$ 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 $\xi$ in $\mathcal{C}$.

Dieser Artikel untersucht Zeitreisen und deren Auswirkungen.

PDF herunterladen: