JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 47-53.doi: 10.6040/j.issn.1671-9352.0.2014.559

Previous Articles     Next Articles

The category of E-quantales

LIANG Shao-hui   

  1. Department of Mathematics, Xi'an University of Science and Technology, Xi'an 710054, Shaanxi, China
  • Received:2014-12-10 Revised:2015-09-06 Online:2015-12-20 Published:2015-12-23

PDF (PC)

604

Abstract: The definition of an E-quantale is introduced, and some properies of E-quantale is obtained. It is proved that the power set of Quantale and the product of E-quantales are E-quantales. Finally, an embedding functor K from the subcategory of Quantales to the category of E-quantale is introducted, and a natural transformation from functor K and forgotten functor U is constructed. Moreover, under some conditions an E-quantale is isomorphic to the power set of a unital Quantale.

Key words: Quantale, category, functor, E-quantale morphisms, natural transformation

CLC Number: 

  • O153.1
[1] MULVEY C J. Second topology conference (Taormina,1984)[J]. Rend Circ Mat Palermo(2): Suppl, 1986, 12:99-104.
[2] MULVEY C J, PELLETIER J W. On the quantisation of point[J]. Journal of Pure and Applied Algebra, 2001, 159:231-295.
[3] NIEFIELD S, ROSENTHAL K I. Strong de Morgan's law and the spectrum of a commutative ring[J]. Journal of Algebra, 1985, 93:169-181.
[4] GIRARD J Y. Linear logic[J]. Theoretical Computer Science, 1987, 50:1-102.
[5] BERNI-CANANI U, BORCEUX F, SUCCI-CRUCIANI R. A theory of quantale sets[J]. Journal of Pure and Applied Algebra, 1989, 62:123-136.
[6] ROSENTHAL K I. Quantales and their applications[M]. London: Longman Scientific and Technical, 1990.
[7] VERMEULEN J J C. Proper maps of locales[J]. Journal of Pure and Applied Algebra, 1994, 92:79-107.
[8] MIRAGLIA F, SOLITRO U. Sheaves over right sided idempotent quantales[J]. Logic J IGPL, 1998, 6(4):545-600.
[9] CONIGLIO M E, MIRAGLIA F. Modules in the category of sheaves over quantales[J]. Annals of Pure and Applied Logic, 2001, 108:103-136.
[10] KRUML D. Spatial quantales[J]. Applied Categorial Structures, 2002, 10: 49-62.
[11] RESENDE P. Sup-lattice 2-forms and quantales[J]. Journal of Algebra, 2004, 276:143-167.
[12] 刘智斌,赵彬. Quantale范畴的代数性[J].数学学报, 2006, 49(6):1253-1258. LIU Zhibin, ZHAO Bin. Algebraic properties of category of quantale[J]. Acta Mathematica Sinica, 2006, 49(6):1253-1258.
[13] 赵斌,梁少辉. 双Quantaler模范畴[J]. 数学学报, 2009, 52(4):821-832. ZHAO Bin, LIANG Shaohui. The category of doubel Quantale modules[J]. Acta Mathematica Sinica, 2009, 52(4) : 821-832.
[14] 梁少辉. L-fuzzy quantale的若干性质[J]. 山东大学学报:理学版,2012,47(4):104-109. LIANG Shaohui. Resarches on some properties of L-fuzzy quantale[J]. Journal of Shandong University: Natural Science, 2012, 47(4):104-109.
[15] LEDDA A, KONIG M, PAOLI F. MV algebras and quantum computation[J]. Studia Logica, 2006, 82(2):245-270.
[16] PASEKA J. Projective quantales: a general view[J]. International Journal of Theoretical Physics, 2008, 47(1):291-296.
[17] REMIGIJUS P G. Extensions of states on MV-quantales[J]. Fuzzy Sets and Systems, 2012, 194:31-51.
[18] TAO Yuantao, LAI Hongliang, ZHANG Dexue. Quantale-valued preorders: Globalization and cocompleteness[J]. Fuzzy Sets and Systems, 2014, 256: 236-251.
[19] RESENDE P. Functoriality of groupoid quantales[J]. Journal of Pure and Applied Algebra, 2015, 219(8):3089-3109.
[20] PULTR A. Notes on an extension of the structure of frame[J]. Discrete Mathematics, 1992, 108(2):107-114.
[21] PICADO J. On extended frames[J]. Commentationes Mathematicae Universitatis Carolinae, 1995, 36(3):537-549.
[22] HERRILICH H, STRECKER E. Category theory[M]. Berlin: Heldermann Verlag, 1979.
[1] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[2] WANG Shou-feng. Prehomomorphisms and restricted products of regular semigroups with a multiplicative inverse transversal [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 90-93.
[3] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[4] LIU Ni, ZHANG Miao-miao. Continuous directed-complete ordered semigroups and their categorical properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 57-64.
[5] FENG Qing, HUANG Ju. Two constructions of monoidal categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 30-34.
[6] SHEN Chong, YAO Wei. A one-to-one correspondence between fuzzy G-ideals and fuzzy Galois connections on fuzzy complete lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 36-41.
[7] LIU Yang1, WANG Zheng-ping2, XU Qing-bing2. The Gabriel monad and the localization of R-module category [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 24-28.
[8] GUO Shuang-jian1, DONG Li-hong2. Engel’s theorem for generalized H-Lie algebras#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 55-57.
[9] LI Hai-yang. The direct limits in the category of closedset lattices [J]. J4, 2013, 48(6): 100-103.
[10] WANG Sheng-xiang1,2, GUO Shuang-jian2. Hom-Hopf modules for a class of symmetric categories [J]. J4, 2013, 48(4): 40-45.
[11] On the quotient category and localization of an R-module Category. On the quotient category and localization of an R-module Category [J]. J4, 2013, 48(4): 46-50.
[12] LIU Min, ZHAO Bin*. Localic nuclei and conuclei on Quantales [J]. J4, 2013, 48(2): 81-87.
[13] DONG Li-hong1,2, GUO Shuang-jian1. The fundamental theorem for weak Hopf module in  Yetter-Drinfeld module categories [J]. J4, 2013, 48(2): 20-22.
[14] CHEN Hua-xi1, ZHANG Xiao-hui2, XU Qing-bing3. The Structure Theorem of weak comodule algebras in
Yetter-Drinfeld module categories [J]. J4, 2013, 48(12): 14-17.
[15] LIU Wu-ying, YI Mian-zhu, ZHANG Xing. A space-time-efficient multi-category text categorization algorithm [J]. J4, 2013, 48(11): 99-104.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd