Georgian Mathematical Journal 13 (2006), No. 4, 635--648
Copyright Heldermann Verlag 2006
Principal Maps in Triangulated Categories and Maps between 2-Stage Spectra
Hans-Joachim Baues
Max-Planck-Institut fuer Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
baues@mpim-bonn.mpg.de
Using two natural axioms on track triangles in triangulated track category we show that the mapping cone construction is functorial, i.e., principal maps between mapping cones in a triangulated category can be identified with the homotopy classes of homotopy pairs. This result is applied to obtain an algebraic model of the category of principal maps between 2-stage spectra.
Keywords: Triangulated categories, groupoid-enriched categories, homotopy pairs, principal maps.
MSC: 18D05, 18E30
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