Complete and directed complete Ω-categories

Theoretical Computer Science

Volumn 388, Issue 1-3, 2007, Pages 1-25

  Lai, Hongliang ^a   Zhang, Dexue ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Commutative quantale; Completeness; Completion; Directed completeness; Enriched category; Weighted colimit; Weighted limit

Indexed keywords

COMPUTER PROGRAMMING;

COMMUTATIVE QUANTALE; COMPLETENESS; DIRECTED COMPLETENESS; ENRICHED CATEGORY; WEIGHTED COLIMIT; WEIGHTED LIMIT;

COMPUTATION THEORY;

EID: 35748952799     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2007.09.012     Document Type: Article

References (32)

1. Abramsky S., and Jung A. Domain theory. In: Abramsky S., et al. (Ed). Handbook of Logic in Computer Science vol. 4 (1994), Oxford University Press 1-168
2. Albert M.H., and Kelly G.M. The closure of a class of colimits. Journal of Pure and Applied Algebra 51 (1998) 1-17
3. Bělohlávek R. Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128 (2004) 277-298
4. Bonsangue M., Breugel F., and Rutten J.J.M.M. Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding. Theoretical Computer Science 193 (1998) 1-51
5. F. Borceux, Handbook of Categorical Algebra, vol. 1, Basic Category Theory, vol. 2, Categories and Structures, Cambridge University Press, 1994
6. Flagg B., and Kopperman R. Continuity spaces: Reconciling domains and metric spaces. Theoretical Computer Science 177 (1997) 111-138
7. Flagg R.C., and Sünderhauf Ph. The essence of ideal completion in quantitative form. Theoretical Computer Science 278 (2002) 141-158
8. R.C. Flagg, Ph. Sünderhauf, K.R. Wagner, A logical approach to quantitative domain theory, Preprint, 1996
9. Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M.W., and Scott D.S. Continuous Lattices and Domains (2003), Cambridge University Press
10. Hájek P. Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publishers, Dordrecht/Boston/London
11. Johnstone P.T. Stone Spaces (1982), Cambridge University Press, Cambridge
12. Kelly G.M. Basic Concepts of Enriched Category Theory. London Mathematical Soceity Lecture Notes Series vol. 64 (1982), Cambridge University Press
13. Kelly G.M., and Schmitt V. Notes on enriched categories with colimits of some class. Theory and Applications of Categories 14 (2005) 399-423
14. Klement E.P., Mesiar R., and Pap E. Triangular Norms. Trends in Logic vol. 8 (2000), Kluwer Academic Publishers, Dordrecht
15. Kock A. Monads for which structures are adjoint to units. Journal of Pure and Apllied Algebra 104 (1995) 41-59
16. Künzi H.P., and Schellekens M.P. On the Yoneda completion of a quasi-metric space. Theoretical Computer Science 278 (2002) 159-194
17. Lawvere F.W. Metric spaces, generalized logic, and closed categories. Rendiconti del Seminario Matématico e Fisico di Milano 43 (1973) 135-166
18. Lawvere F.W. Taking categories seriously. Revisita Columbiana de Matemáticas XX (1986) 147-178
19. Lai H., and Zhang D. Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems 157 (2006) 1865-1885
20. MacLane S. Categories for the Working Mathematician. 2nd ed. (1998), Springer
21. Rosenthal K.I. Quantales and Their Applications (1990), Longman Scientific & Technical
22. Rutten J.J.M.M. Elements of generalized ultrametric domain theory. Theoretical Computer Science 170 (1996) 349-381
23. Rutten J.J.M.M. Weighted colimits and formal balls in general metric spaces. Topology and its Applications 89 (1998) 179-202
24. Schellekens M.P. A characterization of partial metrizability: Domains are quantifiable. Theoretical Computer Science 305 (2003) 409-432
25. V. Schmitt, Flatness, preorders and general metric spaces, preprint, 2006, arXiv:math.CT/0602463
26. Smyth M.B. Quasi-uniformities: Reconciling domains and metric spaces. Lecture Notes in Computer Science vol. 298 (1987), Springer, Berlin 236-253
27. Smyth M.B. Completeness of quasi-uniform and syntopological spaces. Journal of London Mathematical Society 49 2 (1994) 385-400
28. Stubbe I. Categorical structures enriched in a quantaloid: Categories, distributors and functors. Theory and Applications of Categories 14 (2005) 1-45
29. Stubbe I. Categorical structures enriched in a quantaloid: Tensored and cotensored categories. Theory and Applications of Categories 16 (2006) 283-306
30. Vickers S. Localic completion of generalized metric spaces I. Theory and Applications of Categories 14 (2005) 328-356
31. K.R. Wagner, Solving recursive domain equations with enriched categories, Ph.D. Thesis, Carnegie Mellon University, Tech. Report CMU-CS-94-159, July, 1994
32. Wagner K.R. Liminf convergence in Ω-categories. Theoretical Computer Science 184 (1997) 61-104