A Coalgebraic View of Infinite Trees and Iteration |
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| Authors: | Peter Aczel, Ji&#x í Ad mek,Ji&#x í Velebil |
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| Affiliation: | aDepartment of Mathematics and Computer Science, Manchester University, Manchester, United Kingdom;bInstitute of Theoretical Computer Science, Technical University, Braunschweig, Germany;cFaculty of Electrical Engineering, Technical University, Praha, Czech Republic |
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| Abstract: | The algebra of infinite trees is, as proved by C. Elgot, completely iterative, i.e., all ideal recursive equations are uniquely solvable. This is proved here to be a general coalgebraic phenomenon: let H be an endofunctor such that for every object X a final coalgebra, TX, of H(_) + X exists. Then TX is an object-part of a monad which is completely iterative. Moreover, a similar contruction of a “completely iterative monoid” is possible in every monoidal category satisfying mild side conditions. |
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| Keywords: | monad coalgebra monoidal category |
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