Abstract
Let T be a triangulated category and ξ a proper class of triangles. Some basics properties and diagram lemmas are proved directly from the definition of ξ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beligiannis, A.: Relative homological algebra and purity in triangulated categories. J. Algebra, 227, 268–361 (2000)
Beilinson, A. A., Bernstein, J., Deligne, P.: Perverse Sheaves. In: Analysis and Topology on Singular Spaces, I, Luminy, 1981. In: Astérisque, 1982
Bühler, T.: Exact categories. Expo. Math., 28, 1–69 (2010)
Hartshorne, R.: Residues and Duality, Springer-Verlag, Berlin, 1966
Hubery, A.: Notes on the octahedral axiom. Available at http://www.maths.leeds.ac.uk/~ahubery/octahedral.pdf
Iversen, B.: Octahedra and braids. Bull. Soc. Math. France, 114, 197–213 (1986)
Neeman, A.: Triangulated Categories, Princeton Univ. Press, Princeton, NJ, 2001
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by National Natural Science Foundation of China (Grant No. 11001222)
Rights and permissions
About this article
Cite this article
Yang, X.Y. Notes on proper class of triangles. Acta. Math. Sin.-English Ser. 29, 2137–2154 (2013). https://doi.org/10.1007/s10114-013-2435-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-013-2435-2