Tertiary decomposition in Grothendieck categories
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Alain H. M. J. Verschoren (1980)
Czechoslovak Mathematical Journal
Patrik Lundström (2004)
Colloquium Mathematicae
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
Verhaege, P., Verschoren, A. (1998)
Divulgaciones Matemáticas
P. Enache, C. Nastasescu, B. Torrecillas (2006)
Publicacions Matemàtiques
We show the Tychonoff's theorem for a Grothendieck category with a set of small projective generators. Strictly quasi-finite objects for semiartinian Grothendieck categories are characterized. We apply these results to the study of the Morita duality of dual algebra of a coalgebra.
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