Coplexes in abelian categories
DOI:
https://doi.org/10.24193/subbmath.2017.0001Keywords:
Adjoint functors, duality, projective resolution, coplex.Abstract
Starting with a pair F : A +== B : G of additive contravariant functors which are adjoint on the right, between abelian categories, and with a class U , we define the notion of (F, U )-coplex. Considering a reflexive 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 ).
Mathematics Subject Classification (2010): 16E30, 16D90.
References
Al-Nofayee, S., r-Costar pair of contravariant functors, International Journal of Mathematics and Mathematical Sciences, 2012, Article ID 481909, 8 pages.
Al-Nofayee, S., Co-*n-tuple of contravariant functors, British Journal of Mathematics and Computer Science, 4(2014), no. 12, 1701-1709.
Al-Nofayee, S., *s-tuple and *n-tuple of covariant functors, British Journal of Mathematics and Computer Science, 7(2015), no. 6, 439-449.
Breaz, S., Finitistic n-self-cotilting modules, Communications in Algebra, 37(2009), no. 9, 3152-3170.
Breaz, S., Modoi, C., Pop, F., Natural Equivalences and Dualities, Proceedings of the International Conference on Modules and Representation Theory (7-12 July 2008, Cluj- Napoca, Romania), Cluj University Press, 2009, 25-40.
Breaz, S., Pop, F., Dualities Induced by Right Adjoint Contravariant Functors, Stud. Univ. Babe¸s-Bolyai Math., 55(2010), no. 1, 75-83.
Castan˜o-Iglesias, F., On a natural duality between Grothendieck categories, Communications in Algebra, 36(2008), no. 6, 2079-2091.
Colby, R.R., Fuller, K.R., Costar modules, Journal of Algebra, 242(2001), no. 1, 146-159. [9] Colby, R.R., Fuller, K.R., Equivalence and Duality for Module Categories. With Tilting and Cotilting for Rings, Cambridge University Press, Cambridge, 2004.
Faticoni, T.G., A duality for self-slender modules, Communications in Algebra, 35(2007), no. 12, 4175-4182.
Faticoni, T.G., Modules Over Endomorphism Rings, Cambridge University Press, Cam- bridge, 2010.
Fuller, K.R., Natural and doubly natural dualities, Communications in Algebra, 34(2006), no. 2, 749-762.
N˘asta˘sescu, C., Van Oystaeyen, F., Methods of Graded Rings, Lectures Notes in Mathematics 1836, Springer-Verlag, 2004.
Pop, F., Natural dualities between abelian categories, Central European Journal of Mathematics, 9(2011), no. 5, 1088-1099.
Pop, F., Closure properties associated to natural equivalences, Indagationes Mathematicae, 24(2013), no. 2, 403-414.
Wisbauer, R., Cotilting objects and dualities, Representations of algebras, Sao Paulo, 1999, 215-233, Lecture Notes in Pure and Appl. Math., 224, Dekker, New York, 2002.
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