Geodesic
Heller triangulated categories
Homology, homotopy, and applications, Tome 9 (2007) no. 2, pp. 233-320.

Voir la notice de l'article provenant de la source International Press of Boston

Let ${\cal E}$ be a Frobenius category. Let $\underline{\cal E}$ denote its stable category. The shift functor on $\underline{\cal E}$ induces, by pointwise application, an inner shift functor on the category of acyclic complexes with entries in $\underline{\cal E}$. Shifting a complex by $3$ positions yields an outer shift functor on this category. Passing to quotient modulo split acyclic complexes, Heller remarked that inner and outer shift become isomorphic, via an isomorphism satisfying yet a further compatibility. Moreover, Heller remarked that a choice of such an isomorphism determines a Verdier triangulation on $\underline{\cal E}$, except for the octahedral axiom. We generalise the notion of acyclic complexes such that the accordingly enlarged version of Heller’s construction includes octahedra.
DOI : 10.4310/HHA.2007.v9.n2.a10
Classification : 18E30
Keywords: triangulated category 
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     author = {Matthias K\"unzer},
     title = {Heller triangulated categories},
     journal = {Homology, homotopy, and applications},
     pages = {233--320},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n2.a10/}
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Matthias Künzer. Heller triangulated categories. Homology, homotopy, and applications, Tome 9 (2007) no. 2, pp. 233-320. doi : 10.4310/HHA.2007.v9.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n2.a10/

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