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Three results on Frobenius categories

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Abstract

This paper consists of three results on Frobenius categories: (1) we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any Frobenius category is equivalent to an extension-closed exact subcategory of the Frobenius category formed by Cohen–Macaulay modules over some additive category; this is an analogue of Gabriel–Quillen’s embedding theorem for Frobenius categories; (3) we show that under certain conditions an exact category with enough projective and enough injective objects allows a natural new exact structure, with which the given category becomes a Frobenius category. Several applications of the results are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Xiao-Wu Chen

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  1. Xiao-Wu Chen
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Correspondence to Xiao-Wu Chen.

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This project was supported by Alexander von Humboldt Stiftung and National Natural Science Foundation of China (No. 10971206).

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Chen, XW. Three results on Frobenius categories. Math. Z. 270, 43–58 (2012). https://doi.org/10.1007/s00209-010-0785-3

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  • DOI: https://doi.org/10.1007/s00209-010-0785-3

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