Three results on Frobenius categories

Details Three results on Frobenius categories Three results on Frobenius categories

2010-04-26

arxiv.org/abs/1004.4540v1

Mathematics

Representation Theory

16 pages

Scientific paper

10.1007/s00209-010-0785-3

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 Frobenius. Several applications of the results are discussed.

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