Monad compositions i: general constructions and recursive distributive laws

Theory and Applications of Categories

Volumn 18, Issue , 2007, Pages 172-208

  Manes, Ernie ^a   Mulry, Philip ^b  

^a Colgate University ^*  (United States)

^b Assistant Professor in the University Libraries   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247108246     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. Ádamek, J. and Lawvere, F.W., How Algebraic is algebra?, Theory and Applications of Categories 8, 2001, 253-283.
2. Appelgate, H., Acyclic Models and Resolvent Functors, dissertation, Mathematics Department, Columbia University, 1963.
3. Arbib M. A. and Manes E. G., Fuzzy machines in a category, Journal of the Australian Mathematical Society 13, 1975, 169-210.
4. Barr, M., Coequalizers and free triples, Mathematische Zeitschrift 116, 1970, 307-322.
5. Beck, J., Distributive laws, Lecture Notes in Mathematics 80, Springer-Verlag, 1969, 119-140.
6. Bunge, M., Multilinear laws, Comunicaciones Técnicas, Serie Naranja 125, Instituto de Investigaciones en Maternaticas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, 1976.
7. Dubuc, E., Kan Extensions in Enriched Category Theory, Lecture Notes in Mathematics 145, Springer-Verlag, 1970.
8. Eilenberg, S. and Moore, J. C., Adjoint functors and triples, Illinois Journal of Mathematics 9, 1965, 381-398.
9. Gaifmann, H., Infinite Boolean polynomials I, Fundamenta Mathematicae 54, 1964, 229-250.
10. Hales, A. W., On the non-existence of free complete Boolean algebras, Fundamenta Mathematicae 54, 1964, 45-66.
11. Huber, P. J., Homotopy theory in general categories, Mathematisches Annalen 144, 1961, 361-385.
12. Johnstone, P. T., Adjoint lifting theorems for categories of algebras, Bulletin London Mathematical Society 7, 1975, 294-297.
13. Kleisli, H., Every standard construction is induced by a pair of adjoint functors, Proceedings of the American Mathematical Society 16, 1965, 544-546.
14. King, D. and Wadler, P., Combining monads, Functional Programming, Springer Verlag, 1993, 134-143.
15. Kock, A., Strong functors and monoidal monads, Arch. Math. 23, 1972, 113-120.
16. Koslowski, J., A monadic approach to polycategories, Theory and Applications of Categories 14, 2005, 125-156.
17. Linton, F. E. J., Autonomous equational categories, Journal of Mathematics and Mechanics 15, 1966, 637-642.
18. Lüth, C. and Ghani, N. Composing monads using coproducts, ICFP'02, Oct. 4-6, 2002, www.informatik.uni-bremen.de/~cxl/papers/icfp02. pdf.
19. Mac Lane S., Categories for the Working Mathematician, Springer-Verlag, 1971.
20. Manes, E. G., Algebraic Theories, Springer-Verlag, 1976.
21. Manes, E. G., A class of fuzzy theories, Journal of Mathematical Analysis and its Applications 85, 1982, 409-451.
22. Manes E. G., Monads of sets, in M. Hazewinkel (ed.), Handbook of Algebra, Vol. 3, Elsevier Science B.V., 2003, 67-153.
23. Manes, E. G. and Mulry, P. S., Monad compositions II: Kleisli strength, to appear.
24. Manes, E. G. and Mulry, P. S., Monad compositions III: monad approximation, to appear.
25. Marmolejo, F. and Rosebrugh, R. and Wood R. J., A basic distributive law, Journal of Pure and Applied Algebra 168, 2002, 209-226.
26. Meyer J.-P., Induced functors on categories of algebras, Mathematics Department, John Hopkins University, Preprint, 1972.
27. Moggi, E. Notions of computation and monads, Information and Computation 93, 1991, 55-92.
28. Mulry P. S., Lifting theorems for Kleisli categories, Springer Lecture Notes in Computer Science 802, 1994, 304-319.
29. Mulry P. S., Lifting results for categories of algebras, Theoretical Computer Science 278, 2002, 257-269.
30. Street R. S., The formal theory of monads, Journal of Pure and Applied Algebra 2, 1972, 149-168.
31. Wadler, P., The essence of functional programming, Conference Proceedings of the 19th ACM Symposium on Principles of Programming Languages, ACM Press, 1-14, 1992.
32. Wolff, H., Extension of functors to categories of algebras, preprint, circa 1971.