Moghbeli-Damaneh, Halimeh The symmetric monoidal closed category of cpo \(M\)-sets. (English) Zbl 1446.18005 Categ. Gen. Algebr. Struct. Appl. 13, No. 1, 105-124 (2020). Summary: In this paper, we show that the category of directed complete posets with bottom elements (cpos) endowed with an action of a monoid \(M\) on them forms a monoidal category. It is also proved that this category is symmetric closed. MSC: 18B35 Preorders, orders, domains and lattices (viewed as categories) 06F05 Ordered semigroups and monoids 20M30 Representation of semigroups; actions of semigroups on sets 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) Keywords:directed complete partially ordered set; \(M\)-sets; symmetric monoidal closed category PDFBibTeX XMLCite \textit{H. Moghbeli-Damaneh}, Categ. Gen. Algebr. Struct. Appl. 13, No. 1, 105--124 (2020; Zbl 1446.18005) Full Text: Link References: [1] Abramsky, S. and Jung, A., “Domain Theory”, Handbook of Logic in Computer Science 3, Oxford University Press, 1995. [2] Borceux, F., “Handbook of Categorical Algebra 1: Basic Category Theory”, Cambridge University Press, Cambridge, 1994. · Zbl 0803.18001 [3] Borceux, F., “Handbook of Categorical Algebra 2: Categories and Structures”, Cambridge University Press, 1994. · Zbl 0843.18001 [4] Davey, B.A. and Priestly, H.A., “Introduction to Lattices and Order”, Cambridge University Press, 1990. [5] Day, B.J.,On closed categories of functors, Reports of the midwest category seminar (Lane, S.Mac, editor), Lecture Notes in Math. 137 (1970), 1-38. [6] Ebrahimi, M.M. and Mahmoudi, M.,The category of M-Sets, Ital. J. Pure Appl. Math. 9 (2001), 123-132. · Zbl 1008.18004 [7] Fiech, A.,Colimits in the category Dcpo, Math. Structures Comput. Sci., 6 (1996), 455-468. · Zbl 0870.18001 [8] Jung, A., “Cartesian closed categories of Domain”, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1989. [9] Kilp, M., Knauer, U., and Mikhalev, A., “Monoids, Acts and Categories”, Walter de Gruyter, 2000. · Zbl 0945.20036 [10] Mahmoudi, M. and Moghbeli, H.,The category of S-acts in the categoryCpo, Bull. Iran. Math. Soc. 41(1) (2015), 159-175. · Zbl 1344.06012 [11] Mahmoudi, M. and Moghbeli, H.,The categories of actions of a dcpo-monoid on directed complete posets, Quaigroups Related Systems 23 (2015), 283-295. · Zbl 1336.06009 [12] Moghbeli-Damaneh, H.,Actions of a separately cpo-monoid on pointed directed complete posets, Categ. General Alg. Struct. Appl. 3(1) (2015), 21-42. · Zbl 1352.06012 [13] Mac Lane, S., “Categories for the Working Mathematician”, Graduate Texts in Mathematics 5., Springer, 1978. · Zbl 0232.18001 [14] Plotkin, G.D.,A powerdomain construction, SIAM J. Comput. 5 (1976), 452-487. · Zbl 0355.68015 [15] Plotkin, G.D.,A powerdomain for countable non-determinism, In M. Nielsen and E.M. Schmidt, editors, “Automata, Languages and Programming”, Lecture Notes in Computer Sci. 140, pages 412-428. EATCS, Springer Verlage, 1982. · Zbl 0511.68032 [16] Smyth, M.B.,Powerdomains, J. Comput. Systems Sci. 16 (1978), 23-36. [17] Streicher, T., “Domain-theoretic Foundations of Functional Programming”, World Scientific, 2006. · Zbl 1111.68020 [18] Tix, R., Keimel. K., and Plotkin, G.D.,Semantic domains for combining probability and non-determinism, Electron. Notes Theor. Comput. Sci. 222 (2009), 3-99. · Zbl 1271.68005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.