A characterization of closed subfunctors through ($$3\times 3$$)-lemma property in extriangulated categories
Abstract
Abstract Given an extriangulated category $$(\mathcal {C},\mathbb {E},\mathfrak {s})$$ ( C , E , s ) , we introduce the $$(3 \times 3)$$ ( 3 × 3 ) -lemma property for subfunctors of $$\mathbb {E}$$ E and prove that an additive subfunctor $$\mathbb {F}$$ F of $$\mathbb {E}$$ 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 $$\xi $$ ξ in $$\mathcal {C}$$ C .
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Rings
Modules
and Algebras
Publication details
- Journal / source
- Boletín de la Sociedad Matemática Mexicana
- Publisher
- Springer Science and Business Media LLC
- Volume
- 32
- Issue
- 1
- Publication date
- 16 February 2026
- Language
- EN