Morphisms Determined by Objects in Triangulated Categories
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 , 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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