On the monadic nature of categories of ordered sets
Seal, Gavin J.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 52 (2011), p. 163-187 / Harvested from Numdam
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Publié le : 2011-01-01
@article{CTGDC_2011__52_3_163_0,
     author = {Seal, Gavin J.},
     title = {On the monadic nature of categories of ordered sets},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {52},
     year = {2011},
     pages = {163-187},
     mrnumber = {2866502},
     zbl = {1276.18003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2011__52_3_163_0}
}

Seal, Gavin J. On the monadic nature of categories of ordered sets. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 52 (2011) pp. 163-187. http://gdmltest.u-ga.fr/item/CTGDC_2011__52_3_163_0/

[1] J. Beck. Distributive laws. Repr. Theory Appl. Categ., 18:95-112 (electronic), 2008. Reprint of the original [Lect. Notes Math. 80, 119-140 (1969)]. | Zbl 0186.02902

[2] J. Bénabou. Treillis locaux et paratopologies. Séminaire Ehresmann (Topologie et Géometrie Différentielle), 1(2), 1959. | Numdam | MR 121774 | Zbl 0134.40704

[3] F. Borceux. Handbook of Categorical Algebra. 2, volume 51 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1994. Categories and structures. | MR 1313497 | Zbl 0843.18001

[4] A. Day. Filter monads, continuous lattices and closure systems. Canad. J. Math., 27:50-59, 1975. | MR 367013 | Zbl 0436.18003

[5] W. Gähler. Monadic topology-a new concept of generalized topology. In Recent Developments of General Topology and its Applications (Berlin, 1992), volume 67 of Math. Res., pages 136-149. Akademie-Verlag, Berlin, 1992. | MR 1219774 | Zbl 0803.54013

[6] P.T. Johnstone. Stone Spaces, volume 3 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1986. | MR 861951 | Zbl 0586.54001

[7] E. Manes. A Triple Miscellany: some Aspects of the Theory of Algebras overa Triple. PhD thesis, Wesleyan University, 1967. | MR 2617006

[8] E. Manes. A triple theoretic construction of compact algebras. Repr. Theory Appl Categ., 18:73-94 (electronic), 2008. Reprint of the original [Lect. Notes in Math. 80, 91-118 (1969)]. | MR 244342 | Zbl 0186.02901

[9] E.G. Manes. Algebraic Theories, volume 26 of Graduate Texts in Mathematics. Springer, New York, 1976. | MR 419557 | Zbl 0353.18007

[10] F. Marmolejo, R.D. Rosebrugh, and R.J. Wood. A basic distributive law. J. Pure Appl. Algebra, 168(2-3):209-226, 2002. Category theory 1999 (Coimbra). | MR 1887158 | Zbl 1005.18006

[11] M.C. Pedicchio and W. Tholen. Multiplicative structures over suplattices. Arch. Math., 25(1-2): 107-114, 1989. | MR 1189206 | Zbl 0717.18003

[12] M.C. Pedicchio and R.J. Wood. Groupoidal completely distributive lattices. J. Pure Appl. Algebra, 143(1-3):339-350, 1999. | MR 1731051 | Zbl 0936.18004

[13] C. Schubert. Lax Algebras-A Scenic Approach. PhD thesis, Universität Bremen, 2006. | Zbl 1302.18002

[14] C. Schubert and G.J. Seal. Extensions in the theory of lax algebras. Theory Appl. Categ., 21(7): 118-151, 2008. | MR 2476848 | Zbl 1165.18005

[15] G.J. Seal. Order-adjoint monads and injective objects. J. Pure Appl. Algebra, 214:778-796, 2010. | MR 2580657 | Zbl 1203.18009

[16] M. Sobral. CABool is monadic over almost all categories. J. Pure Appl. Algebra, 77(2):207-218, 1992. | MR 1149022 | Zbl 0761.18007

[17] O. Wyler. Algebraic theories of continuous lattices. In Proc. Conf., Bremen 1979, volume 871 of Lecture Notes in Math., pages 390-413. Springer, Berlin, 1981.