Elgot theories: A new perspective on the equational properties of iteration

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00179252" target="_blank" >RIV/68407700:21230/11:00179252 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0960129510000496" target="_blank" >http://dx.doi.org/10.1017/S0960129510000496</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129510000496" target="_blank" >10.1017/S0960129510000496</a>

Result language
angličtina
Original language name
Elgot theories: A new perspective on the equational properties of iteration
Original language description
Bloom and Ésik's concept of iteration theory summarises all equational properties that iteration has in common applications, for example, in domain theory, where to every system of recursive equations, the least solution is assigned. This paper shows that in the coalgebraic approach to iteration, the more appropriate concept is that of a functorial iteration theory (called Elgot theory). These theories have a particularly simple axiomatisation, and all well-known examples of iteration theories are functorial. Elgot theories are proved to be monadic over the category of sets in context (or, more generally, the category of finitary endofunctors of a locally finitely presentable category). This demonstrates that functoriality is an equational property from the perspective of sets in context. In contrast, Bloom and Ésik worked in the base category of signatures rather than sets in context, and there iteration theories are monadic
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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