Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Quasi-symmetric B-categories

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
This paper deals with B-categories where B is a quantaloid obtained from a right Gelfand quantale Q. Quantale is non-commutative extension of concept of locale. A notion of sheaf for Q is introduced; it turns out that these sheaves are precisely quasi-symmetric skeletal Cauchy-complete B-categories. In particular if Q is a locale, this construction reduces to that given in ”Sheaves and Cauchy-complete Categories” by R.F.C. Walters.
Opis fizyczny
Bibliogr. 21 poz.
  • Balochistan University of Information Technology and Management Sciences (Buitms) Samungli Road Jinnah Town, Quetta, Pakistan,
  • [1] J. Benabou, Introduction to bicategoires, Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, Springer, Berlin, 1967.
  • [2] G. Birkhoff, J. V. Neumann, The logic of quantum mechanics, Ann. Math. 37, No. 4, October, 1936.
  • [3] F. Borceux, About quantales and quantic spaces, The University of Sydney, Sydney Category Seminar Reports, 1984.
  • [4] F. Borceux, I. Stubbe, Short Introduction to Enriched Categories, in: Current Research in Operational Quantum Logic, Kluwer Academic Publishers, Dordrecht, 2000, pp. 167-194.
  • [5] F. Borecux and G. Van Den Bossche, Quantales and their sheaves, Order 3, 61 (1986).
  • [6] M. P. Fourman and D. S. Scott, Sheaves and Logic, Applications of Sheaves, Lecture Notes in Mathematics, Springer, Heidelberg, 1979.
  • [7] D. Kruml, J .W. Palleteir, P. Resende, J. Rosicky, On quantales and spectras of C*-algebras, Applied Categorical Structures Volume 11, Number 6, December 2003, pp. 543-560.
  • [8] F. W. Lawvere, Metric spaces, generalized logic and closed categories, Rend. Sem. Mat. Fuis. Milano 43, pp. 135-166.
  • [9] F. Miraglia, U. Solitro, Sheaves on the right sided idempotent quantales, Logic Journal of the IGPL Vol. No. 4, pp. 545-600, 1998.
  • [10] C. J. Mulvey, M. Nawaz, Quantales: Quantal sets, Theory and Decision Library, Series B: Mathematical and Statistical Methods Volume 32, Non-Classical Logics And Their Applications To Fuzzy Subsets, edited by Ulrich Hohle and Eric Peter Klement, Kluwer Academic Publishers, Netherlands. pp. 159-217, 1995.
  • [11] C. J. Mulvey, &, Suppl. Rend. Circ. Mat. Palermo 12, pp. 99-104, 1986.
  • [12] C. J. Mulvey, J. W. Palletier, On quantization of points, J. Pure Appl. Algebra 175 (2001), 289-325.
  • [13] C. J. Mulvey, P. Resende, A noncommutatice theory of Penrose tilings, Intern. J. Theoret. Phys., vol. 44, Number 6, June 2005, pp. 655-689.
  • [14] M. Nawaz, Quantales: Quantal Sets, D. Phil. thesis, University of Sussex, September 1985.
  • [15] K. I. Rosenthal, The Theory of Quantaloids, Pitman Research Notes in Mathematics Series. Longman, Harlow 1996.
  • [16] I. Stubbe, Categorical structures enriched in a quantaloid: categories and semicategories, thesis, Universite de Catholique de Louvain, November, 2003.
  • [17] I. Stubbe, Categorical structures enriched in a quantaloid: categories, distributors and functors, Theory Appl. Categ. 14 (2005), 1-45.
  • [18] I. Stubbe, Categorical structures enriched in a quantaloid: tensored and cotensored categories, Theory Appl. Categ. 16 (2006), 283-306.
  • [19] I. Stubbe, Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories, Cahiers Topologie G´eom. Diff´erentielle Cat´egoriques 46 (2005), 99-121.
  • [20] I. Stubbe, Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid, Applied Categorical Structures 13 (2005), 235-255.
  • [21] R. F. C. Walters, Sheaves and Cauchy-complete categories, Cahiers Topologie Géom. Differentielle vol. XXII-3 (1981), 283-286.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.