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A triangulated category is an additive category equipped with the additional structure of an autoequivalence (called the translation functor) and a class of of triangles satisfying certain axioms.
17
votes
Pre-triangulated category that isn't triangulated
I have to say that this article
http://arxiv.org/abs/1506.00887
has at least one mistake.
Lemma 3.5,
Counterexample - take group $G=$ sequences of integer numbers $=\mathbb{Z}^\mathbb{N}$.
$\ell$ an …