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Triangulated track categories. (English) Zbl 1155.18004

In the article the notion of triangulated homotopy categories will be advanced to the level of groupoid-enriched categories in a canonical way. The classical concept of triangulation of a category will be lifted to the new concept of triangulation of track categories. A triangulated track category is an additive track category with a translation track functor and a distinguished class of track triangles satisfying two natural axioms which replace the four axioms of a triangulated category. Triangulated track categories always have a homotopy category which is triangulated in the classical sense. In this manner a description of good morphisms between exact triangles in the sense of Neeman is obtained.

MSC:

18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
18G55 Nonabelian homotopical algebra (MSC2010)
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