Almost split sequences in tri-exact categories
Representation Theory
2020-07-01 v1
Abstract
We shall study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories of triangulated categories. Our results unify and extend the existence theorems for almost split sequences in abelian categories and exact categories (that is, extension-closed subcategories of abelian categories), and those for almost split triangles in triangulated categories. As applications, we shall obtain some new results on the existence of almost split sequences in the derived categories of all modules over an algebra with a unity or a locally finite dimensional algebra given by a quiver with relations.
Cite
@article{arxiv.2006.16451,
title = {Almost split sequences in tri-exact categories},
author = {Shiping Liu and Hongwei Niu},
journal= {arXiv preprint arXiv:2006.16451},
year = {2020}
}