Exactness of cochain complexes via additive functors
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1075-1085
Published online September 7, 2020
Printed October 31, 2020
Federico Campanini, Alberto Facchini
Universit\`a di Padova; Universit\`a di Padova
Abstract : We investigate the relation between the notion of $e$-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\Mod R\to \Spec(\Mod R)$, where $\Spec(\Mod R)$ denotes the spectral category of $\Mod R$, and the localization functor with respect to the singular torsion theory.
Keywords : Relative exactness of sequences, spectral category
MSC numbers : Primary 16E30
Supported by : The second author is supported by Ministero dell’Istruzione, dell’Universit? e della Ricerca(Progetto di ricerca di rilevante interesse nazionale “Categories, Algebras: Ring-Theoretical and Homological Approaches (CARTHA)”) and Dipartimento di Matematica “Tullio Levi-Civita” of Universit? di Padova (Research program DOR1828909 “Anelli e categorie dimoduli”).
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