The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver
Bernhard Keller
Université Paris 7 Centre for Mathematics UFR de Mathématiques and its Applications Institut de Mathématiques Mathematical Sciences Institute UMR 7586 du CNRS John Dedman Building Case 7012 The Australian National University 2, place Jussieu Canberra, ACT 0200 75251 Paris Cedex 05 Australia FranceAmnon Neeman
Université Paris 7 Centre for Mathematics UFR de Mathématiques and its Applications Institut de Mathématiques Mathematical Sciences Institute UMR 7586 du CNRS John Dedman Building Case 7012 The Australian National University 2, place Jussieu Canberra, ACT 0200 75251 Paris Cedex 05 Australia France
Abstract
In an important recent paper citeMay01, May gave an axiomatic description of the properties of triangulated categories with a symmetric tensor product. The main point of the current article is that there are two other results in the literature which can be used to shed considerable light on May's work. The first is a construction of Verdier's, which appeared in Beilinson, Bernstein and Deligne's cite[Prop. 1.1.11, pp. 24-25]BeiBerDel82. The second and more important is the beautiful work of Happel, in citeHappel87, which can be used to better organise May's axioms.
Cite this article
Bernhard Keller, Amnon Neeman, The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver . Doc. Math. 7 (2002), pp. 535–560
DOI 10.4171/DM/131