Extensions in the theory of lax algebras

Theory and Applications of Categories

Volumn 21, Issue , 2008, Pages 118-151

  Schubert, Christoph ^a   Seal, Gavin J ^b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Initial extension; Kleisli extension; Lax algebra; Strata extension; Tower extension

Indexed keywords

EID: 55849145848     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. J. Adámek, H. Herrlich, and G.E. Strecker. Abstract and concrete categories: The joy of cats. Repr. Theory Appl. Categ., (17): 1-507 (electronic), 2006. Reprint of the 1990 original.
2. M. Barr. Relational algebras. In Reports of the Midwest Category Seminar, IV, number 137 in Lecture Notes in Mathematics, pages 39-55. Springer, 1970.
3. M.M. Clementino and D. Hofmann. On extensions of lax monads. Theory Appl. Categ., 13(3):41-60 (electronic), 2004.
4. M.M. Clementino, D. Hofmann, and W. Tholen. One setting for all: Metric, topology, uniformity, approach structure. Appl. Categ. Structures, 12(2): 127-154, 2004.
5. E. Colebunders and R. Lowen. Lax monads and algebras via initial monad morphisms. 2007. Preprint.
6. A. Day. Filter monads, continuous lattices and closure systems. Canad. J. Math., 27:50-59, 1975.
7. B. Fawcett and R.J. Wood. Constructive complete distributivity. I. Math. Proc. Camb. Phil. Soc., 107(1):81-89, 1990.
8. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. Continuous Lattices and Domains. Number 93 in Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2003.
9. F. Hausdorff. Grundzüge der Mengenlehre. Chelsea, 1949.
10. D. Hofmann. Topological theories and closed objects. Adv. Math., 215(2):789-824, 2007.
11. D. Hofmann and W. Tholen. Kleisli operations for topological spaces. Topology Appl., 153(15):2952-2961, 2006.
12. U. Höhle. Many Valued Topology and its Applications. Kluwer, Boston, 2001.
13. E. Lowen and R. Lowen. Topological quasitopos hulls of categories containing topological and metric objects. Cahiers Top. et Géom. Diff., 30(3):213-228, 1989.
14. R. Lowen. Approach Spaces. Oxford Mathematical Monographs. Oxford University Press, New York, 1997. The missing link in the topology-uniformity- metric triad.
15. E.G. Manes. Algebraic Theories. Springer-Verlag, New York, 1976. Graduate Texts in Mathematics, No. 26.
16. E.G. Manes. Taut monads and TO-spaces. Theoret. Comput. Sci., 275(1-2):79-109, 2002.
17. K.I. Rosenthal. The Theory of Quantaloids, volume 348 of Pitman Research Notes in Mathematics Series. Longman, Harlow, 1996.
18. C. Schubert. Lax Algebras - A Scenic Approach. PhD thesis, Universität Bremen, 2006.
19. G.J. Seal. Canonical and op-canonical lax algebras. Theory Appl. Categ., 14(10):221-243 (electronic), 2005.
20. G.J. Seal. A Kleisli-based approach to lax algebras. Appl. Categ. Structures, 2007. To appear.
21. D. Zhang. Tower extension of topological constructs. Comment. Math. Univ. Carolin., 41(1):41-51, 2000.