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On the Stability Question of Gorenstein Categories

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Abstract

In this paper we are interested in studying the stability question of subcategories of an abelian category \(\mathcal {A}\) constituted of all objects that admit (proper) coproper resolutions (resp. (coproper) proper coresolutions) with terms in a subcategory \(\mathcal {E}\) of \(\mathcal {A}\). Using a new approach, we give an affirmative answer to the stability question on these categories under the condition that \(\mathcal {E}\) is closed under finite direct sums. This result generalizes Huang’s affirmative answer to the well-known stability question of Gorenstein categories raised by Sather-Wagstaff, Sharif and White. We end the paper with an example showing that the condition imposed on \(\mathcal {E}\) cannot be dropped.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

    Driss Bennis

  2. Department of Mathematics, University of Almería, 04071, Almería, Spain

    J. R. García Rozas & Luis Oyonarte

Authors
  1. Driss Bennis
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  2. J. R. García Rozas
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  3. Luis Oyonarte
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Corresponding author

Correspondence to Driss Bennis.

Additional information

The last two authors were partially supported by the grant MTM2014-54439-P from Ministerio de Economía y Competitividad.

We authors wish to dedicate this paper to Edgar Enochs. His influence in our lives cannot be expressed with words: we started our joint work when we were just beginner researchers and this collaboration has lasted around twenty years, until Ed’s retirement, so we can truly say that we are what we are in part thanks to Ed’s advice. But by no means less important has been the personal influence that his character has left in our daily lives. For all this we wish to express now our gratitude and recognition to him.

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Bennis, D., García Rozas, J.R. & Oyonarte, L. On the Stability Question of Gorenstein Categories. Appl Categor Struct 25, 907–915 (2017). https://doi.org/10.1007/s10485-016-9478-3

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  • DOI: https://doi.org/10.1007/s10485-016-9478-3

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