Epimorphisms and closure operators of categories of semilattices

References

• J. Adámek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories. The Joy of Cats, online edition, http://katmat.math.uni-bremen.de/acc/acc.pdf, 2005.
   Google Scholar
• P. Arduini, Monomorphisms and epimorphisms in abstract categories, Rend. Sem. Mat. Univ. Padova 42 (1969), 135–166.
   Google Scholar
• S. Baron, Note on epi in T0, Canad. Math. Bull. 11 (1968), 503–504. doi: 10.4153/CMB-1968-061-6
   Web of Science ®Google Scholar
• G. Birkhoff, Lattice Theory, In: AMS Colloquium Publications, Vol. 25, American Mathematical Society, Providence, RI, 1984.
   Google Scholar
• I. Castellano, D. Dikranjan, D. Freni, A. Giordano Bruno, and D. Toller, Intrinsic entropy for generalized quasi-metric semilattices, J. Algebra Appl. 21(10) (2022), 2250244. doi: 10.1142/S0219498822502449
   Google Scholar
• I. Castellano, A. Giordano Bruno, and N. Zava, Weakly weightable generalized quasi-metric spaces and semilattices, Theor. Comput. Sci., https://doi.org/10.1016/j.tcs.2023.114129.
   Google Scholar
• G. Castellini, Categorical closure operators, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 2003.
   Google Scholar
• D. Dikranjan, Closure operators related to von Neumann’s kernel, Topology Appl. 153(11) (2006), 1930–1955. doi: 10.1016/j.topol.2005.02.014
   Web of Science ®Google Scholar
• D. Dikranjan and A. Giordano Bruno, Entropy on normed semigroups, Diss. Math. 542 (2019), 1–90.
   Google Scholar
• D. Dikranjan, A. Giordano Bruno, H.-P. Künzi, D. Toller, and N. Zava, Generalized quasi-metric semilattices, Topology Appl. 309 (2022), Paper No. 107916. doi: 10.1016/j.topol.2021.107916
   Web of Science ®Google Scholar
• D. Dikranjan and E. Giuli, Closure operators induced by topological epireflections, Coll. Math. Soc. J. Bolyai 43 (1983), 233–246.
   Google Scholar
• D. Dikranjan and E. Giuli, Closure operators I, Topology Appl. 27 (1987), 129–143. doi: 10.1016/0166-8641(87)90100-3
   Web of Science ®Google Scholar
• D. Dikranjan and E. Giuli, Factorizations, injectivity and compactness in categories of modules, Comm. Alg. 19 (1991), 45–83. doi: 10.1080/00927879108824129
   Web of Science ®Google Scholar
• D. Dikranjan, E. Giuli, and W. Tholen, Closure operators II, Categorical topology and its relation to analysis, algebra and combinatorics (Prague, 1988) pp. 297–335, World Sci. Publ., Teaneck, NJ, 1989.
   Google Scholar
• D. Dikranjan and J. Pelant, The impact of closure operators on the structure of a concrete category, Quaest. Math. 18 (1995), 381–396. doi: 10.1080/16073606.1995.9631810
   Google Scholar
• D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators with Applications to Topology, Algebra and Discrete Mathematics, Mathematics and its Applications, Vol. 346, Kluwer Acad. Publ., Dordrecht/Boston/London 1995. doi: 10.1007/978-94-015-8400-5
   Google Scholar
• D. Dikranjan, W. Tholen, and S. Watson, Classification of closure operators for categories of topological spaces, Categorical structures and their applications, pp. 69–98, World Sci. Publ., River Edge, NJ, 2004.
   Google Scholar
• D. Dikranjan and S. Watson, The category of S(α)-spaces is not cowellpowered, Topology Appl. 61(2) (1995), 137–150. doi: 10.1016/0166-8641(94)00033-Y
   Web of Science ®Google Scholar
• D. Dikranjan and S. Watson, Finite posets and their closure operators, Preprint, August 1997.
   Google Scholar
• D. Dikranjan and N. Zava, Some categorical aspects of coarse spaces and balleans, Topology Appl. 225 (2017), 164–194. doi: 10.1016/j.topol.2017.04.011
   Web of Science ®Google Scholar
• E. Giuli and M. Hušek, A diagonal theorem for epireflective subcategories of Top and cowellpoweredness, Ann. Mat. Pura Appl. 145(4) (1986), 337–346. doi: 10.1007/BF01790546
   Google Scholar
• E. Giuli, S. Mantovani, and W. Tholen, Objects with closed diagonals, J. Pure Appl. Algebra 51(1–2) (1988), 129–140. doi: 10.1016/0022-4049(88)90083-7
   Web of Science ®Google Scholar
• E. Giuli and P. Simon, On spaces in which every bounded subset is Hausdorff, Topology Appl. 37(3) (1990), 267–274. doi: 10.1016/0166-8641(90)90025-W
   Web of Science ®Google Scholar
• H. Herrlich, Topologische Reflexionen und Coreflexionen, Lecture Notes in Mathematics, No. 78 Springer-Verlag, Berlin/New York, 1968.
   Google Scholar
• H. Herrlich, Limit-operators and topological coreflections, Trans. Amer. Math. Soc. 146 (1969), 203–210. doi: 10.1090/S0002-9947-1969-0252473-2
   Web of Science ®Google Scholar
• H. Herrlich, Epireflective subcategories of TOP need not be cowellpowered, Comm. Math. Univ. Carolinae 16(4) (1975), 713–716.
   Google Scholar
• H. Herrlich, G. Salicrup, and G. Strecker, Factorizations, denseness, separation, and relatively compact objects, Topology Appl. 27(2) (1987), 157–169. doi: 10.1016/0166-8641(87)90102-7
   Web of Science ®Google Scholar
• H. Herrlich and G. Strecker, Category theory: an introduction, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass., 1973.
   Google Scholar
• A. Horn and N. Kimura, The category of semilattices, Algebra Universalis 1(1) (1971), 26–38. doi: 10.1007/BF02944952
   Google Scholar
• J.M. Howie and J. Isbell, Epimorphisms and dominions II, J. Algebra 6 (1967), 7–21. doi: 10.1016/0021-8693(67)90010-5
   Web of Science ®Google Scholar
• J. Isbell, Epimorphisms and dominions, In: Proc. Conf. Categorical Algebra, La Lolla, 1965, pp. 232–246, Springer, Berlin 1966.
   Google Scholar
• J. Isbell, Epimorphisms and dominions IV, Proc. London Math. Soc. s2–1(1) (1969), 265–273. doi: 10.1112/jlms/s2-1.1.265
   Google Scholar
• S.G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences-Paper Edition 728 (1994), 183–197. doi: 10.1111/j.1749-6632.1994.tb44144.x
   Google Scholar
• Y. Nakamura, Entropy and semivaluations on semilattices, Kodai Math. Sem. Rep. 22(4) (1970), 443–468. doi: 10.2996/kmj/1138846220
   Google Scholar
• S. Salbany, Reflective subcategories and closure operators, Lecture Notes in Mathematics, Vol. 540, pp. 548–565, Springer-Verlag, Berlin/Heidelberg/New York, 1976.
   Google Scholar
• M.P. Schellekens, The correspondence between partial metrics and semivaluations, Th. Computer Science 315 (2004), 135–149. doi: 10.1016/j.tcs.2003.11.016
   Web of Science ®Google Scholar
• J. Schröder, The category of Urysohn spaces is not cowellpowered, Topology Appl. 16(3) (1983), 237–241. doi: 10.1016/0166-8641(83)90020-2
   Web of Science ®Google Scholar
• L. Skula, On a reflective subcategory of the category of all topological spaces, Trans. Amer. Math. Soc. 142 (1969), 37–41.
   Web of Science ®Google Scholar
• W. Tholen, Diagonal theorems in topology and elsewhere, General topology and its relations to modern analysis and algebra, VI (Prague, 1986), Res. Exp. Math., Vol. 16, pp. 559–566, Heldermann, Berlin, 1988.
   Google Scholar
• V. Uspenskij, The epimorphism problem for Hausdorff topological groups, Topology Appl. 57 (1994), 287–294. doi: 10.1016/0166-8641(94)90055-8
   Web of Science ®Google Scholar
• N. Zava, Cowellpoweredness and closure operators in categories of coarse spaces, Topology Appl. 268 (2019), 106899. doi: 10.1016/j.topol.2019.106899
   Web of Science ®Google Scholar