Bases for Parametrized Iterativity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F08%3A03145472" target="_blank" >RIV/68407700:21230/08:03145472 - 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
Bases for Parametrized Iterativity
Original language description
Parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables (chosen as a parameter). We show how such algebras can be introduced in anarbitrary category A by employing a base, i.e., an operation interpreting objects of A as monads on A. For every base we prove that free base algebras and free iterative base algebras exist. The main result is a coalgebraic construction of the latter: all equation morphisms form a diagram whose colimit is proved to be a free iterative base algebra.
Czech name
Báze pro parametrizovanou iterativitu
Czech description
Parametrizovana iterativita algebry znamena existenci jedineho reseni vsech finitarnich rekursivnich systemu rovnic, kde rekurse je dovolena pouze jistym promennym (zvolenym a priori libovolne). Ukazujeme, jak lze v libovolne kategorii A takove algebry zavest pomoci baze; tj. pomoci operace, interpretujici objekty A jako monady na A. Ukazujeme, ze volne algebry a volne iterativni algebry existuji pro kazdou bazi. Hlavnim vysledkem je koalgebraicka konstrukce volnych iterativnich algeber: vsechny systemyrovnic tvori diagram, jehoz kolimitou je volna iterativni algebra nad danou bazi.

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
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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