Totally Acyclic Approximations

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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Correspondence to David A. Jorgensen.

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Communicated by Henning Krause.

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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