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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 assignment in 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. The reason 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 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 assignment in 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. The reason 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 (en)
Title	Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) (en)
skos:prefLabel	Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) (en)
skos:notation	RIV/68407700:21230/09:00157080!RIV10-MSM-21230___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6840770014)
http://linked.open...iv/cisloPeriodika	249
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Velebil, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	312999
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/09:00157080
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	iteration theory; Elgot theory; iterative algebra; rational monad (en)
http://linked.open.../riv/klicoveSlovo	iteration theory Elgot theory iterative algebra rational monad
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[B2136242D0F2]
http://linked.open...i/riv/nazevZdroje	Electronic Notes in Theoretical Computer Science
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	2009
http://linked.open...iv/tvurceVysledku	Velebil, Jiří
http://linked.open...n/vavai/riv/zamer	Výzkum perspektivních informačních a komunikačních technologií
issn	1571-0661
number of pages	21 (xsd:int)
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract) Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)

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