Localic triquotient maps are effective descent maps

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 122, Issue 1, 1997, Pages 17-43

  Plewe, Till ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

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[No Author keywords available]

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EID: 21744451690     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0305004196001648     Document Type: Article

References (32)

1. B. BANASCHEWSKI. Another look at the localic Tychonoff theorem. Comment. Math. Univ. Carolin. 29 (1988), 647-656.
2. B. BANASCHEWSKI. Singly generated frame extensions. J. Pure Appl. Alg. 83 (1990), 1-21.
3. M. BARR and C. WELLS. Toposes, triples and theories. Grundlehren der mathematischen Wissenschaften 278 (Springer, 1985).
4. B. J. DAY and G. M. KELLY. On topological quotient maps preserved by pullbacks or products. Proc. Camb. Phil. Soc. 67 (1970), 553-558.
5. C. H. DOWKER and D. STRAUSS. Sums in the category of frames. Houston J. Math. 3 (1977), 17-32.
6. O. HÁJEK. Notes on quotient maps. Comment. Math. Univ. Carolin. 7 (1906), 319-323.
7. O. HÁJEK. Corrections to notes on quotient maps. Comment. Math. Univ. Carolin. 8 (1967), 171.
8. J. R. ISBELL. Atomless parts of spaces. Math. Scand. 31 (1972), 623-626.
9. J. R. ISBELL. First steps in descriptive theory of locales. Trans. Amer. Math. Soc. 327 (1991), 353-371.
10. G. JANELIDZE and W. THOLEN. How algebraic is the change of base functor? In Proc. Conf. Category theory, Como, 1990, Lecture Notes in Mathematics, vol. 1488 (Springer, 1991), 174-186.
11. P. T. JOHNSTONE. Tychonoff's theorem without the axiom of choice. Fund. Math. 113 (1981), 21-35.
12. P. T. JOHNSTONE. Stone Spaces. (Cambridge Univ. Press, 1982).
13. P. T. JOHNSTONE. A constructive 'closed subgroup theorem ' for localic groups and groupoids. Cahiers Top. Geom. Diff. Cat. 30 (1989), 2-23.
14. P. T. JOHNSTONE and S.-H. SUN. Weak products and Hausdorff locales; in Categorical Algebra and its Applications, Lecture Notes in Mathematics, vol. 1348 (Springer, 1988), 173-193.
15. P. T. JOHNSTONE and S. VICKERS. Preframe presentations present; in Proc. Conf. Category theory, Como, 1990, Lecture Notes in Mathematics, vol. 1488 (Springer, 1991) 193-212.
16. A. JOYAL and M. TIERNEY. An extension of the Galois theory of Grothendieck. Memoirs of the Amer. Math. Soc. No. 309, vol. 51, 1984.
17. I. KŘÍŽ. A constructive proof of the Tychonoff's theorem for locales. Comment. Math. Univ. Carolin. 26 (1985), 619-630.
18. S. MACLANE. Categories for the working mathematician. (Springer, 1971).
19. E. MICHAEL. Bi-quotient maps and cartesian products of quotient maps. Ann. Inst. Fourier, Grenoble 18 (1968), 287-302.
20. E. MICHAEL. Complete spaces and triquotient maps. Ill. J. Math. 21 (1977), 716-733.
21. E. MICHAEL and A. H. STONE. Quotients of the spaces of irrationals. Pac. J. Math. 28 (1969), 629-633.
22. I. MOERDIJK. Continuous fibrations and inverse limits of toposes. Compositio Math 58 (1986), 45-72.
23. I. MOERDIJK. Note on descent for proper maps of topological spaces (manuscript).
24. I. MOERDIJK. Descent theory for toposes. Bull. Soc. Math. Belgique 41 (1989), 373-391.
25. T. PLEWE. Localic product of spaces, to appear in Proc. London Math. Soc.
26. δ-spaces, to appear in Top. Appl.
27. J. REITERMAN and W. THOLEN. Effective descent maps of topological spaces. Top. Appl. 57 (1994), 53-69.
28. V. V. USPENSKII. Tri-quotient maps are preserved by infinite products, to appear in Proc. Amer. Math. Soc.
29. J. J. C. VERMEULEN. Some constructive results related to compactness and the (strong) Hausdorff property for locales; in Proc. Conf. Category theory, Como, 1990, Lecture Notes in Mathematics, vol. 1488 (Springer, 1991), 401-409.
30. J. J. C. VERMEULEN. A note on iterative arguments in a topos. Math. Proc. Camb. Phil. Soc. 111 (1992), 57-62.
31. J. J. C. VERMEULEN. Proper maps of locales. J. Pure Appl. Alg. 92 (1994), 79-107.
32. D. WIGNER. Two notes on frames. J. Austral. Math. Soc. (Series A) 28 (1979), 257-268.