For ideal monads in Set (e. g. the finite list monad, the finite bag monad etc.) we have recently proved that every set generates a free iterative algebra. This gives rise to a new monad. We prove now that this monad is iterative in the sense of Calvin Elgot, in fact, this is the iterative reflection of the given ideal monad. This shows how to freely add unique solutions of recursive equations to a given algebraic theory. Examples: the monad of free commutative binary algebras has the monad of binary rational unordered trees as iterative reflection, and the finite list monad has the iterative reflection given by adding an absorbing element. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Adámek, J., Milius, S., & Velebil, J. (2009). A description of iterative reflections of monads (EXTENDED ABSTRACT). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5504 LNCS, pp. 152–166). https://doi.org/10.1007/978-3-642-00596-1_12
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