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|Paper IPM / M / 16933||
Let \CC be a locally bounded \k-category, where \k is a field. It is proved that \CC is pure-semisimple, i.e., every object of \Mod \CC is pure-projective, if and only if every family of morphisms between indecomposable finitely generated \CC-modules is noetherian. Our formalism establishes the pure-semisimplicity of Galois coverings, that is, if \CC is a G-category with a free G-action on \ind \CC, then \CC is pure-semisimple if and only if \CC/G is so.
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