Coplexes in abelian categories

Flaviu Pop

Abstract


Starting with a pair F:A-><-B:G of additive and contravariant functors which are adjoint on the right, between abelian categories, and with a class UU, we define the notion of (F,UU)-coplex, and considering an object U of A with F(U)=V projective object in B, we construct a natural duality between the category of all (F, add(U))-coplexes in A and the subcategory of B consisting in all objects in B which admit a projective resolution with all terms in the class add(V).

Keywords


adjoint functors;duality;projective resolution;coplex

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References


Breaz S, Finitistic n-cotilting modules, Comm. Algebra, 2009, 37(9),3152-3170;

Castano-Iglesias F., On a natural duality between Grothendieck categories, Comm. Algebra, 2008, 36(6), 2079-2091;

Faticoni T.G., A duality for self-slender modules, Comm. Algebra, 2007, 35(12), 4175-4182;

Pop F., Natural dualities between abelian categories, Cent. Eur. J. Math., 2011, 9(5), 1088-1099.




DOI: http://dx.doi.org/10.24193/subbmath.2017.0001

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