Totally Acyclic Approximations

Applied Categorical Structures (2021)Cite this article

Abstract

Let \(Q \rightarrow R\) be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as a Q-bimodule admits a finite resolution by modules which are projective on both sides. We define an adjoint pair of functors between the homotopy category of totally acyclic R-complexes and that of Q-complexes. This adjoint pair is analogous to the classical adjoint pair of functors between the module categories of R and Q. As a consequence, we obtain a precise notion of approximations of totally acyclic R-complexes by totally acyclic Q-complexes.

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Acknowledgements

The authors would like to thank the anonymous referee for multiple useful comments.

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Affiliations

  1. Institutt for matematiske fag, NTNU, 7491, Trondheim, Norway

    Petter A. Bergh

  2. Department of mathematics, University of Texas at Arlington, Arlington, TX, 76019, USA

    David A. Jorgensen

  3. Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC, 27109, USA

    W. Frank Moore

Authors
  1. Petter A. Bergh
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  2. David A. Jorgensen
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  3. W. Frank Moore
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Correspondence to David A. Jorgensen.

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Bergh, P.A., Jorgensen, D.A. & Moore, W.F. Totally Acyclic Approximations. Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09633-1

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Keywords

  • Totally acyclic complex
  • Approximation
  • Adjoint functors

Mathematics Subject Classification

  • 16E05
  • 18G80
  • 16E65