On regular and homological closure operators
Clementino, Maria Manuel ; Gutierres, Gonçalo
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 51 (2010), p. 127-142 / Harvested from Numdam
Publié le : 2010-01-01
@article{CTGDC_2010__51_2_127_0,
     author = {Clementino, Maria Manuel and Gutierres, Gon\c calo},
     title = {On regular and homological closure operators},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {51},
     year = {2010},
     pages = {127-142},
     mrnumber = {2667980},
     zbl = {1216.18002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2010__51_2_127_0}
}
Clementino, Maria Manuel; Gutierres, Gonçalo. On regular and homological closure operators. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 51 (2010) pp. 127-142. http://gdmltest.u-ga.fr/item/CTGDC_2010__51_2_127_0/

[1] A. Arhangel'Skiĭ; and R. Wiegandt, Connectednesses and disconnectednesses in Topology, Gen. Topology and Appl. 5 (1975), 9-33. | MR 367920 | Zbl 0329.54008

[2] F. Borceux and D. Bourn, Mal'cev, protomodular, homological and semi-abelian categories, Mathematics and its Applications, 566. Kluwer Academic Publishers, Dordrecht, 2004. | MR 2044291 | Zbl 1061.18001

[3] F. Borceux and M. M. Clementino, Topological semi-abelian algebras, Adv. Math. 190 (2005), no. 2, 425-453. | MR 2102663 | Zbl 1069.54010

[4] F. Borceux, M. M. Clementino, M. Gran and L. Sousa, Protolocalisations of homological categories, J. Pure Appl. Algebra 212 (2008), 1898-1927. | MR 2414694 | Zbl 1151.18012

[5] D. Bourn, Normal subobjects and abelian objects in protomodular categories, J. Algebra 228 (2000), 143-164. | MR 1760960 | Zbl 0969.18008

[6] D. Bourn and M. Gran, Torsion theories and closure operators, J. Algebra 305 (2006), 18-47. | MR 2262518 | Zbl 1123.18009

[7] M. M. Clementino, Weakly hereditary regular closure operators, Topology Appl. 49 (1993), 129-139. | MR 1206220 | Zbl 0781.18001

[8] M. M. Clementino, D. Dikranjan and W. Tholen, Torsion theories and radicals in normal categories, J. Algebra 305 (2006), 98-129. | MR 2262521 | Zbl 1121.18010

[9] M. M. Clementino and W. Tholen, Separation versus connectedness, Topology Appl. 75 (1997), no. 2, 143-181. | MR 1427747 | Zbl 0906.18003

[10] S. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235. | MR 191935 | Zbl 0138.01801

[11] D. Dikranjan, E. Giuli and W. Tholen, Closure Operators II, in: Proc. Int. Conf. on Categorical Topology, Prague 1988 (World Scientific, Singapore 1989), pp. 297-335. | MR 1047909

[12] D. Dikranjan and W. Tholen, Categorical structure of closure operators. With applications to topology, algebra and discrete mathematics, Mathematics and its Applications, 346, Kluwer, Dordrecht, 1995. | MR 1368854 | Zbl 0853.18002

[13] G. Gutierres, On coregular closure operators, Preprint 99-21, Department of Mathematics, University of Coimbra (1999), http://www.mat.uc.pt/preprints/1999.html.

[14] G. Janelidze, L. Márki and W. Tholen, Semi-abelian categories, J. Pure Appl. Algebra 168 (2002), no. 2-3, 367-386. | MR 1887164 | Zbl 0993.18008

[15] S. Salbany, Reflective subcategories and closure operators, in: Lecture Notes in Math. (Springer 1976), pp. 548-565. | MR 451186 | Zbl 0335.54003