Almost split sequences and approximations

Abstract

Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. First, we give new characterizations of an almost split sequence in A, which yields some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence inAinduces an almost split sequence in an exact subcategory C of A. In case A has almost split sequences and C is Ext-finite and Krull-Schmidt, we obtain a necessary and sufficient condition for C to have almost split sequences. Finally, we show some applications of these results. © Springer Science+Business Media Dordrecht 2012.