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Functors and Morphisms Determined by Subcategories

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Abstract

We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a \({{\,\mathrm{Hom}\,}}\)-finite hereditary abelian category with enough projectives, we prove that the Auslander–Reiten–Smalø–Ringel formula of the minimal right determiner still holds. As an application, we give a formula of minimal right determiners in the category of finitely presented representations of strongly locally finite quivers.

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Acknowledgements

This project is under the guidance of Professor Gordana Todorov. The author will thank Charles Paquette and Shiping Liu for helpful discussions at the \(\hbox {XXVII}\)th Meeting on Representation Theory of Algebras; Dan Zacharia for his hospitality during my visit at Syracuse University; as well as Yingdan Ji for pointing out mistakes during the seminars. The author also would like to thank the anonymous referee for the helpful comments and pointing out some recent related references.

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  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Shijie Zhu

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  1. Shijie Zhu
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Correspondence to Shijie Zhu.

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Communicated by Henning Krause.

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Zhu, S. Functors and Morphisms Determined by Subcategories. Appl Categor Struct 28, 381–417 (2020). https://doi.org/10.1007/s10485-019-09585-7

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  • DOI: https://doi.org/10.1007/s10485-019-09585-7

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