English

Three results on Frobenius categories

Representation Theory 2013-11-11 v1

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 Frobenius. Several applications of the results are discussed.

Keywords

Cite

@article{arxiv.1004.4540,
  title  = {Three results on Frobenius categories},
  author = {Xiao-Wu Chen},
  journal= {arXiv preprint arXiv:1004.4540},
  year   = {2013}
}

Comments

16 pages

R2 v1 2026-06-21T15:14:55.035Z