Completely iterative algebras and completely iterative monads

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Completely iterative algebras and completely iterative monads

Completely iterative theories of Calvin Elgot formalize (potentially infinite) computations as solutions of recursive equations. One of the main results of Elgot and his coauthors is that infinite trees form a free completely iterative theory. Their algebraic proof of this result is extremely complicated. We present completely iterative algebras as a new approach to the description of free comp...

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Completely continuous Banach algebras

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

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Infinite trees and completely iterative theories: a coalgebraic view

In#nite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has #nal coalgebras for all functors H ( ) + X , then those coalgebras, TX , form a monad. This monad is complet...

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ژورنال

عنوان ژورنال: Information and Computation

سال: 2005

ISSN: 0890-5401

DOI: 10.1016/j.ic.2004.05.003