Baues, Hans-Joachim Triangulated track categories. (English) Zbl 1155.18004 Georgian Math. J. 13, No. 4, 607-634 (2006). 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. Reviewer: Bernhard Drabant (Mühlhausen) Cited in 1 Document MSC: 18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) 18E30 Derived categories, triangulated categories (MSC2010) 18G55 Nonabelian homotopical algebra (MSC2010) Keywords:triangulated categories; groupoid-enriched categories; track categories PDFBibTeX XMLCite \textit{H.-J. Baues}, Georgian Math. J. 13, No. 4, 607--634 (2006; Zbl 1155.18004)