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Abstract: This paper consists of three results on Frobenius categories: 1 we givesufficient conditions on when a factor category of a Frobenius category isstill a Frobenius category; 2 we show that any Frobenius category isequivalent to an extension-closed exact subcategory of the Frobenius categoryformed by Cohen-Macaulay modules over some additive category; this is ananalogue of Gabriel-Quillen-s embedding theorem for Frobenius categories; 3we show that under certain conditions an exact category with enough projectiveand enough injective objects allows a natural new exact structure, with whichthe given category becomes Frobenius. Several applications of the results arediscussed.



Author: Xiao-Wu Chen

Source: https://arxiv.org/







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