On the elementary theory of Heller triangulated categories

Matthias Künzer
Verdier's formalism of triangulated categories works with triangles, which fit into octahedra. These triangles enjoy a morphism prolongation property, but those octahedra do not. We establish a formalism of n-triangles such that the 2-triangles coincide with Verdier's triangles, such that the 3-triangles are particular Verdier octahedra, and such that n-triangles appear for all n. Now morphism prolongation holds for all n. Following Heller, we let the n-triangles be governed by an isotransformation between two shift...
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