Almost split sequences and approximations
Category Theory
2012-03-23 v1 Representation Theory
Abstract
Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence in A induces an almost split sequence in an exact subcategory C of A. In case A has almost split sequences and C is Hom-finite Krull-Schmidt, this provides a necessary and sufficient condition for C to have almost split sequences. Finally, we show two applications of these results.
Keywords
Cite
@article{arxiv.1203.5009,
title = {Almost split sequences and approximations},
author = {Shiping Liu and Puiman Ng and Charles Paquette},
journal= {arXiv preprint arXiv:1203.5009},
year = {2012}
}
Comments
16 pages