Coproducts of ideal monads

Ghani, Neil; Uustalu, Tarmo

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 4, pp. 321-342.

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1-83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18-32], and that of Hyland, Plotkin and Power [IFIP Conf. Proc. 223 (2002) 474-484], we are looking for specific situations when simpler constructions are available. This paper uses fixed points to give a simple construction of the coproduct of two ideal monads.

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