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.
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