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Some remarks on categories of modules modulo morphisms with essential kernel or superfluous image. (English) Zbl 1293.16005

The authors work with preadditive category \(\mathcal A\). They prove that for an ideal \(\mathcal I\) of \(\mathcal A\) there is a largest full subcategory \(\mathcal C\) of \(\mathcal A\) such that the canonical functor \(C\colon\mathcal C\to\mathcal C/\mathcal I\) is local. An additive functor \(F\) between preadditive categories is called local when a morphism \(f\) in \(\mathcal A\) is an isomorphism if its image \(F(f)\) is an isomorphism. This result has several consequences when the category \(\mathcal C\) together with the ideal \(\mathcal I\) are specialized as module categories with certain ideals. The authors discuss also the extension of their results from the case of one ideal to the case of finitely many ideals.

MSC:

16D90 Module categories in associative algebras
18E05 Preadditive, additive categories
18A22 Special properties of functors (faithful, full, etc.)
16W20 Automorphisms and endomorphisms
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