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No-iteration mixed distributive laws

Published online by Cambridge University Press:  20 February 2015

F. MARMOLEJO  and
A. VÁZQUEZ-MÁRQUEZ
F. MARMOLEJO
Affiliation:
Instituto de Matemáticas, Área de la Investigación Científica, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F. 04510, México
A. VÁZQUEZ-MÁRQUEZ
Affiliation:
Instituto de Matemáticas, Área de la Investigación Científica, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F. 04510, México
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Abstract

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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.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Issue 1 , January 2017 , pp. 1 - 16
Copyright
Copyright © Cambridge University Press 2015 

References

Beck, J. (1969) Distributive laws. In: Seminar on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67) Springer, Berlin 119–140.Google 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.Google 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.Google 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.Google 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.Google 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.Google 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.Google Scholar
Walters, R. F. C. (1970) A Categorical Approach to Universal Algebra, Ph.D. thesis, Australian National University.Google Scholar