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arXiv · 1203.5009

Almost split sequences and approximations

Shiping Liu·Puiman Ng·Charles Paquette
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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.

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Shiping Liu, Puiman Ng, Charles Paquette. 2012-03-19. Almost split sequences and approximations. https://arxiv.org/abs/1203.5009

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