### Heller triangulated categories, by Matthias Kuenzer

Update to preprint no. 784. Appeared in Homology, Homotopy and Applications,
vol. 9 (2), 233-320, 2007.

Let E be a Frobenius category, let _E_ denote its stable category.
The shift functor on _E_ induces a first shift functor
on the category of acyclic complexes with entries in _E_ by pointwise
application. Shifting a complex by 3 positions yields a second shift
functor on this category. Passing to the quotient modulo split
acyclic complexes, Heller remarked that these two shift functors
become isomorphic, via an isomorphism satisfying still a further
compatibility. Moreover, Heller remarked that a choice of such an
isomorphism determines a triangulation on _E_, except for the
octahedral axiom. We generalize the notion of acyclic complexes
such that the accordingly enlarged version of Heller's construction
includes octahedra.

Matthias Kuenzer <kuenzer@math.rwth-aachen.de>