JournalsdmVol. 7pp. 535–560

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, UFR de Mathématiques, Institut de Mathématiques, UMR 7586 du CNRS, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France
    ORCID

  • Amnon Neeman

    Centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, The Australian National University, Canberra, ACT 0200, Australia
    ORCID
The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver $D_4$ cover
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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.

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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