The double powerlocale and exponentiation: A case study in geometric logic

Theory and Applications of Categories

Volumn 12, Issue 1, 2004, Pages 372-422

  Vickers, Steven ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Exponentiable; Geometric logic; Locale; Powerlocale

Indexed keywords

EID: 18544386070     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. [AbrVic 93] Abramsky, S., and Vickers, S. J. "Quantales, Observational Logic and Process Semantics". Mathematical Structures in Computer Science 3 (1993), 161-227.
2. [Beck 69] Beck, J. "Distributive laws", in Springer Lecture Notes in Mathematics 80 (1969), 119-140.
3. [FoScott 79] Fourman, M.P., and Scott, D.S. "Sheaves and Logic", in Applications of Sheaves - Proceedings of Durham Symposium, 1977 (Springer Lecture Notes in Mathematics 753, 1979), 302-410.
4. [Hyland 81] Hyland, J.M.E. "Function spaces in the category of locales", in Banaschewski and Hoffmann (eds) Continuous lattices (Springer Lecture Notes in Mathematics 871, 1981), 264-281.
5. [Johnstone 77] Johnstone, P.T. Topos Theory. Academic Press, London, 1977.
6. [Johnstone 82] Johnstone, P.T. Stone Spaces, Cambridge Studies in Advanced Mathematics 3. Cambridge University Press, 1982.
7. [JoVic 91] Johnstone, P.T., and Vickers, S.J. "Preframe presentations present", in Carboni, Pedicchio and Rosolini (eds) Category Theory - Proceedings, Como, 1990 (Springer Lecture Notes in Mathematics 1488, 1991), 193-212.
8. [JoyTie 84] Joyal, A. and Tierney, M. An Extension of the Galois Theory of Grothendieck, Memoirs of the American Mathematical Society 309, 1984.
9. [Kock 95] Kock, A. "Monads for which structures are adjoint to units", Journal of Pure and Applied Algebra 104 (1995), 41-59.
10. [MRW] Marmolejo, F., Rosebrugh, R.D., and Wood, R.J. "A basic distributive law". To appear in Journal of Pure and Applied Algebra.
11. [Sambin 87] Sambin, G., "Intuitionistic formal spaces - a first communication", in Skordev (ed) Mathematical logic and its applications, Plenum, 1987, 187-204.
12. [Smyth 77] Smyth, M. "Effectively given domains", Theoretical Computer Science 5 (1977), 257-274.
13. [Taylor 01] Taylor, P. "Sober spaces and continuations", in preparation. Draft available at http://www.dcs.qmul.ac.uk/~pt/ASD/.
14. [Vickers 89] Vickers, S. J. Topology via Logic, Cambridge University Press, 1989.
15. [Vickers 93] Vickers, S.J. "Information systems for continuous posets". Theoretical Computer Science 114 (1993), 201-229.
16. [Vickers 95] Vickers, S.J. "Locales are not pointless", in Hankin, Mackie and Nagarajan (eds) Theory and Formal Methods of Computing 1994 (Imperial College Press, 1995) 199-216.
17. [Vickers 97] Vickers, S.J. "Constructive points of powerlocales". Math. Proc. Cam. Phil. Soc. 122 (1997), 207-222.
18. [Vickers 99] Vickers, S.J. "Topical categories of domains". Mathematical Structures in Computer Science 9 (1999), 569-616.
19. [Vickers 01] Vickers, S.J. "Strongly Algebraic = SFP (Topically)". To appear in Mathematical Structures in Computer Science.