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The axioms for \(n\)-angulated categories. (English) Zbl 1272.18008

A triangulated category is an additive category with an automorphism together with the datum of so-called distinguished triangles subject to several axioms. For instance, the derived category of complexes over an abelian category is triangulated.
Now, \(n\)-angulated categories, introduced by Geiss, Keller and Oppermann, are a generalization of the above concept. Roughly speaking, triangles become sequences of length \(n\) while keeping appropriate versions of the axioms. In the paper under review the authors discuss how the first two (of four) original axioms in the definition of an \(n\)-angulated category can be replaced by equivalent ones. Furthermore, the original fourth axiom (the mapping cone axiom) is checked to be equivalent to a higher octahedral axiom introduced in this paper. In the case \(n=3\) the authors show that the mapping cone, the higher octahedral and the original octahedral axiom are equivalent.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
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References:

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