Morphisms Determined by Objects in Triangulated Categories

Part of the Abel Symposia book series (ABEL, volume 8)


The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of this concept arises from a reformulation of Freyd’s generating hypothesis.



Some 20 years ago, Maurice Auslander encouraged me (then a postdoc at Brandeis University) to read his Philadelphia notes [1], commenting that they had never really been used. More recently, postdocs at Bielefeld asked me to explain this material; I am grateful to both of them. Special thanks goes to Greg Stevenson for helpful discussions and comments on a preliminary version of this paper, and to Apostolos Beligiannis for sharing interest in this subject.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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