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No-iteration mixed distributive laws
Published online by Cambridge University Press: 20 February 2015
Abstract
We present the no-iteration version of a mixed distributive law of a monad over a comonad in a general 2-category. We present the simplifications that occur in the case of the 2-category Cat.
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References
Beck, J. (1969) Distributive laws. In: Seminar on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67)
Springer, Berlin
119–140.CrossRefGoogle Scholar
Brzeziński, T. and Majid, S. (1998) Coalgebra bundles. Communications in Mathematical Physics
191
(2)
467–492.Google Scholar
Burroni, E. (1973) Lois distributives mixtes.
Comptes Rendus de l'Académie des Sciences – Series A
276
897–900.Google Scholar
Manes, E. (1976) Algebraic Theories, Berlin-Heidelberg-New York: Springer-Verlag.CrossRefGoogle Scholar
Manes, E. (2003) Monads of sets. In: Hazewinkel, M. (ed.) Handbook of Algebra, volume 3, Amsterdam, The Netherlands: Elsevier Science.Google Scholar
Marmolejo, F. (1998) Continuous families of coalgebras. Journal of Pure and Applied Algebra
130
(2)
197–215.CrossRefGoogle Scholar
Marmolejo, F. (1999) Doctrines whose structure forms a fully faithful adjoint string. Theory and Applications of Categories
3
(2)
24–44.Google Scholar
Marmolejo, F. and Wood, R. J. (2010) Monads as extension systems – no iteration is necessary.
Theory and Applications of Categories
24
84–113.Google Scholar
Moggi, E. (1991) Notions of computations and monads. Information and Computation
93
(1)
55–92.CrossRefGoogle Scholar
Power, J. and Watanabe, H. (2002) Combining a monad and a comonad. Coalgebraic methods in computer science (Amsterdam, 1999). Theoretical Computer Science
280
(1–2)
137–162.CrossRefGoogle Scholar
Street, R. H. (1972) The formal theory of monads.
Journal of Pure and Applied Algebra
2
149–168.CrossRefGoogle Scholar
Turi, D. and Plotkin, G. (1997) Towards a mathematical operational semantics. In: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, LICS '97, IEEE Computer Society Press
280–291.Google Scholar
Uustalu, T. and Vene, V. (2008) Comonadic notions of computation. Electronic Notes in Theoretical Computer Science
203
263–284.CrossRefGoogle Scholar
VanOsdol, Donovan H. (1971) Sheaves in regular categories. In: Exact Categories and Categories of Sheaves, Lecture Notes in Mathematics volume 236, Berlin-Heidelberg-New York: Springer-Verlag
223–239.CrossRefGoogle Scholar
Walters, R. F. C. (1970) A Categorical Approach to Universal Algebra, Ph.D. thesis, Australian National University.Google Scholar