Iterative algebras at work
- Autores: Jirí Adámek, Stefan Milius, Jiri Velebi
- Localización: Mathematical structures in computer science, ISSN 0960-1295, Vol. 16, Nº 6, 2006, págs. 1085-1131
- Idioma: inglés
- DOI: 10.1017/s0960129506005706
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Resumen
Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations. One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees. Their algebraic proof of this fact is extremely complicated. In our paper we show that by starting with ¿iterative algebras¿, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras. The (coalgebraic) proof we present is dramatically simpler than the original algebraic one. Despite this, our result is much more general: we describe a free iterative theory on any finitary endofunctor of every locally presentable category $\cal{A}$.
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