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Relatively divisible and relatively flat objects in exact categories: applications

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Abstract

For a Quillen exact category \({\mathcal {C}}\) endowed with two exact structures \({\mathcal {D}}\) and \({\mathcal {E}}\) such that \({\mathcal {E}}\subseteq {\mathcal {D}}\), an object X of \({\mathcal {C}}\) is called \({\mathcal {E}}\)-divisible (respectively \({\mathcal {E}}\)-flat) if every short exact sequence from \({\mathcal {D}}\) starting (respectively ending) with X belongs to \({\mathcal {E}}\). We continue our study of relatively divisible and relatively flat objects in Quillen exact categories with applications to finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Septimiu Crivei

  2. Department of Mathematics, Hacettepe University, 06800, Beytepe Ankara, Turkey

    Derya Keskin Tütüncü

Authors
  1. Septimiu Crivei
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  2. Derya Keskin Tütüncü
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Correspondence to Derya Keskin Tütüncü.

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Crivei, S., Keskin Tütüncü, D. Relatively divisible and relatively flat objects in exact categories: applications. AAECC 32, 365–384 (2021). https://doi.org/10.1007/s00200-021-00487-7

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