## 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:

 1.8e+31 Derived categories, triangulated categories (MSC2010)
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### References:

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