Continuous categories revisited

Theory and Applications of Categories

Volumn 11, Issue 1, 2003, Pages 252-282

  Adamek J ^a   Lawvere, F W ^b   Rosicky J ^c  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b UNIVERSITY AT BUFFALO   (United States)

^c MASARYK UNIVERSITY   (Czech Republic)

Author keywords

Continuous lattice; Locally finitely presentable category; Precontinuous category; Pseudomonad

Indexed keywords

EID: 0742285300     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. [AGV] M. Artin, A. Grothendieck and J. L. Verdier, Théorie des topos et cohomologie étale des schémas, Lect. Notes in Math. 269, Springer-Verlag, Berlin 1972.
2. [AKT] J. Adámek, V. Koubek and V. Trnková, How large are left exact functors, Theory and Applications of Categories 8(13), 2001, 377-390.
3. [ALR] J. Adámek, F. W. Lawvere and J. Rosický, How algebraic is algebra, Theory and Applications of Categories 8(9), 2001, 253-283.
4. [AR] J. Adámek and J. Rosický, Locally presentable and accessible categories, Cambridge Univ. Press 1994.
5. [ARV] J. Adámek, J. Rosický and E. M. Vitale, On algebraically exact categories and essential localizations of varieties, J. Alg. 244 (2001), 450-477.
6. [B] J. Beck, Distributive laws, Lect. Notes in Math. 80 (1969), 119-140.
7. A. Day, Filter monads, continuous lattices and closure systems, Canad. J. Math. 27 (1975), 50-59.
8. [Do] H.-D. Donder, Regularity of ultrafilters and the core model, Israel J. Math. 63 (1988), 289-322.
9. [DS] B. Day and R. Street, Monoidal bicategories and Hopf algebroids, Adv. Math. 129 (1997), 99-157.
10. [JJ] P. Johnstone and A. Joyal, Continuous categories and exponentiable toposes, J. Pure Appl. Algebra 25 (1982), 255-296.
11. [K] A. Kock, Monads for which structures are adjoint to units, J. Pure Appl. Alg. 104 (1995), 41-59.
12. 1] F. W. Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Soc. 50 (1963), 865-872.
13. 2] F. W. Lawvere, Ordinal sums and equational doctrines, Lect. Notes in Math. 80 (1969), 141-155.
14. 1] F. Marmolejo, Doctrines whose structure forms a fully faithful adjoint string, Theory and Applications of Categories 3(2) 1997, 24-44.
15. 2] F. Marmolejo, Distributive laws for pseudomonads, Theory and Applications of Categories 5(5) 1999, 91-147.
16. 3] F. Marmolejo, Distributive laws for pseudomonads II, to appear.
17. F. Marmolejo, I. J. Le Creurer and E. M. Vitale, Beck's theorem for pseudo-monads, to appear.
18. [MRW] F. Marmolejo, R. D. Rosebrugh and R. J. Wood, A basic distributive law, J. Pure Appl. Alg. 168 (2002), 209-226.
19. [R] J. Reiterman, An example concerning set functors, Comm. Math. Univ. Carol. 12 (1971), 227-233.
20. [T] V. Trnková, On descriptive classification of set functors I, Comm. Math. Univ. Carolinae 12 (1971), 143-173.
21. [W] O. Wyler, Algebraic theories of continuous lattices, In: Continuous lattices (ed. B. Banaschewski and R.-E. Hoffmann), Lecture Notes in Math. 871, 390-413, Springer Verlag, Berlin 1981.