In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
@article{bwmeta1.element.doi-10_2478_s11533-011-0048-5,
author = {Flaviu Pop},
title = {Natural dualities between abelian categories},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1088-1099},
zbl = {1245.18003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0048-5}
}
Flaviu Pop. Natural dualities between abelian categories. Open Mathematics, Tome 9 (2011) pp. 1088-1099. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0048-5/
[1] Azumaya G., A duality theory for injective modules, Amer. J. Math., 1959, 81(1), 249–278 http://dx.doi.org/10.2307/2372855 | Zbl 0088.03304
[2] Breaz S., Almost-flat modules, Czechoslovak Math. J., 2003, 53(128)(2), 479–489 http://dx.doi.org/10.1023/A:1026255908301
[3] Breaz S., A Morita type theorem for a sort of quotient categories, Czechoslovak Math. J., 2005, 55(130)(1), 133–144 http://dx.doi.org/10.1007/s10587-005-0009-x
[4] Breaz S., Finitistic n-self-cotilting modules, Comm. Algebra, 2009, 37(9), 3152–3170 http://dx.doi.org/10.1080/00927870902747639 | Zbl 1205.16004
[5] Breaz S., Modoi C., On a quotient category, Studia Univ. Babeş-Bolyai Math., 2002, 47(2), 17–28 | Zbl 1027.16007
[6] Breaz S., Modoi C., Pop F., Natural equivalences and dualities, In: Proceedings of the International Conference on Modules and Representation Theory, Cluj-Napoca, July 7–12, 2008, Presa Universitară Clujeană, Cluj-Napoca, 2009, 25–40 | Zbl 1194.16008
[7] Breaz S., Pop F., Dualities induced by right adjoint contravariant functors, Studia Univ. Babeş-Bolyai Math., 2010, 55(1), 75–83 | Zbl 1208.16013
[8] Castaño-Iglesias F., On a natural duality between Grothendieck categories, Comm. Algebra, 2008, 36(6), 2079–2091 http://dx.doi.org/10.1080/00927870801949534 | Zbl 1153.16005
[9] Colby R.R., Fuller K.R., Costar modules, J. Algebra, 2001, 242(1), 146–159 http://dx.doi.org/10.1006/jabr.2001.8784
[10] Colby R.R., Fuller K.R., Equivalence and Duality for Module Categories, Cambridge Tracts in Math., 161, Cambridge University Press, Cambridge, 2004 http://dx.doi.org/10.1017/CBO9780511546518 | Zbl 1069.16001
[11] Colpi R., Fuller K.R., Cotilting modules and bimodules, Pacific J. Math., 2000, 192(2), 275–291 http://dx.doi.org/10.2140/pjm.2000.192.275 | Zbl 1014.16008
[12] Fuller K.R., Natural and doubly natural dualities, Comm. Algebra, 2006, 34(2), 749–762 http://dx.doi.org/10.1080/00927870500388059 | Zbl 1099.16001
[13] Gabriel P., Des catégories abéliennes, Bull. Soc. Math. France, 1962, 90, 323–448 | Zbl 0201.35602
[14] Mantese F., Tonolo A., Natural dualities, Algebr. Represent. Theory, 2004, 7, 43–52 http://dx.doi.org/10.1023/B:ALGE.0000019385.66745.59 | Zbl 1069.16011
[15] Morita K., Duality for modules and its applications to the theory of rings with minimum conditions, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 1958, 6, 83–142 | Zbl 0080.25702
[16] Năstăsescu C., Torrecillas B., Morita duality for Grothendieck categories with applications to coalgebras, Comm. Algebra, 2005, 33(11), 4083–4096 http://dx.doi.org/10.1080/00927870500261397 | Zbl 1101.16031
[17] Năstăsescu C., Van Oystaeyen F., Methods of Graded Rings, Lecture Notes in Math., 1836, Springer, Berlin, 2004 | Zbl 1043.16017
[18] Tonolo A., On a finitistic cotilting type duality, Comm. Algebra, 2002, 30(10), 5091–5106 http://dx.doi.org/10.1081/AGB-120014686 | Zbl 1017.16003
[19] Wakamatsu T., Tilting modules and Auslander’s Gorenstein property, J. Algebra, 2004, 275(1), 3–39 http://dx.doi.org/10.1016/j.jalgebra.2003.12.008 | Zbl 1076.16006
[20] Wisbauer R., Cotilting objects and dualities, In: Representations of Algebras, São Paulo, 1999, Lecture Notes in Pure and Appl. Math., 224, Marcel Dekker, New York, 2002, 215–233
[21] Wisbauer R., Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach, Philadelphia, 1991 | Zbl 0746.16001