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On the K-theory of \(\mathbb {Z}\)-categories

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Abstract

We establish connections between the concepts of Noetherian, regular coherent, and regular n-coherent categories for \(\mathbb {Z}\)-linear categories with finitely many objects and the corresponding notions for unital rings. These connections enable us to obtain a negative K-theory vanishing result, a fundamental theorem, and a homotopy invariance result for the K-theory of \(\mathbb {Z}\)-linear categories.

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Notes

  1. In [3], the word right is omitted, but we have chosen to include it in our notation.

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Acknowledgements

Eugenia Ellis was partially supported by ANII. Both authors were partially supported by PEDECIBA, CSIC and by the grant ANII FCE-3-2018-1-148588. We would like to thank Willie Cortiñas and Carlos E. Parra for their interesting comments and discussions. We also thank to the referee for their corrections and comments.

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  1. IMERL, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Eugenia Ellis & Rafael Parra

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  1. Eugenia Ellis
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  2. Rafael Parra
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Correspondence to Eugenia Ellis.

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Communicated by Guillermo Cortinas.

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Ellis, E., Parra, R. On the K-theory of \(\mathbb {Z}\)-categories. J. Homotopy Relat. Struct. 18, 455–476 (2023). https://doi.org/10.1007/s40062-023-00333-2

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  • DOI: https://doi.org/10.1007/s40062-023-00333-2

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