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An Explicit Ladder of Homotopy Categories

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Abstract

For an upper triangular matrix ring, an explicit ladder of height 2 of triangle functors between homotopy categories is constructed. Under certain conditions, the author obtains a localization sequence of homotopy categories of acyclic complexes of injective modules.

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Acknowledgements

The author is grateful to her supervisor Professor Xiao-Wu Chen for his guidance and encouragement. The author thanks Pengjie Jiao for helpful discussion. The author thanks the anonymous referees for their very helpful suggestions to improve this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Huanhuan Li

  2. Centre for Research in Mathematics, Western Sydney University, Sydney, New SouthWales, Australia

    Huanhuan Li

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  1. Huanhuan Li
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Correspondence to Huanhuan Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11522113, 11571329).

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Li, H. An Explicit Ladder of Homotopy Categories. Chin. Ann. Math. Ser. B 41, 209–226 (2020). https://doi.org/10.1007/s11401-020-0195-8

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  • DOI: https://doi.org/10.1007/s11401-020-0195-8

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