Almost Split Sequences and Approximations

作者：Liu Shiping^*; Ng Puiman; Paquette Charles

来源：Algebras and Representation Theory, 2013, 16(6): 1809-1827.

DOI：10.1007/s10468-012-9383-x

• Krull-Schmidt categories
• Exact categories
• Almost split sequences
• Approximations
• Functorially finite subcategories
• Non-degenerate bilinear forms

Let 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 , which yields some necessary and sufficient conditions for to have almost split sequences. Then, we study when an almost split sequence in induces an almost split sequence in an exact subcategory of . In case has almost split sequences and is Ext-finite and Krull-Schmidt, we obtain a necessary and sufficient condition for to have almost split sequences. Finally, we show some applications of these results.

• 出版日期2013-12