Abstract
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.
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Notes
- 1.
This result is not correct as stated; the term \(P(\operatorname{Coker} \alpha )\) needs to be modified, as pointed out by Ringel in [14].
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Acknowledgements
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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Krause, H. (2013). Morphisms Determined by Objects in Triangulated Categories. In: Buan, A., Reiten, I., Solberg, Ø. (eds) Algebras, Quivers and Representations. Abel Symposia, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39485-0_9
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