Alahmadi, Adel; Facchini, Alberto Some remarks on categories of modules modulo morphisms with essential kernel or superfluous image. (English) Zbl 1293.16005 J. Korean Math. Soc. 50, No. 3, 557-578 (2013). 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. Reviewer: Ánh Pham Ngoc (Budapest) Cited in 5 Documents MSC: 16D90 Module categories in associative algebras 18E05 Preadditive, additive categories 18A22 Special properties of functors (faithful, full, etc.) 16W20 Automorphisms and endomorphisms Keywords:preadditive categories; additive functors; local functors; morphisms with essential kernels; morphisms with superfluous images PDFBibTeX XMLCite \textit{A. Alahmadi} and \textit{A. Facchini}, J. Korean Math. Soc. 50, No. 3, 557--578 (2013; Zbl 1293.16005) Full Text: DOI Link