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>