Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00157080" target="_blank" >RIV/68407700:21230/09:00157080 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)
Original language description
The concept of iteration theory of Bloom and ´Esik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignmentin Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pity: functorial iteration theories have a particularly simple axiomatization, and most of examples of iteration theories are functorial. Thereason for excluding functoriality was the view that this property cannot be called equational. This is true from the perspective of the category Sgn of signatures as the base category: whereas iteration theories are monadic (thus, equationally presentable) over Sgn, functorial iteration theories are not. In the present paper we propose to change the perspective and work, in lieu of Sgn, in the category of sets in context (the presheaf category of finite sets and functions). We p
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
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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