Initial algebras and terminal coalgebras in many-sorted sets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104336" target="_blank" >RIV/00216208:11320/11:10104336 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0960129510000502" target="_blank" >http://dx.doi.org/10.1017/S0960129510000502</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129510000502" target="_blank" >10.1017/S0960129510000502</a>

Result language
angličtina
Original language name
Initial algebras and terminal coalgebras in many-sorted sets
Original language description
We prove that the iterative construction of initial algebras converges for endofunctors F of many-sorted sets whenever F has an initial algebra. In the case of one-sorted sets, the convergence takes n steps where n is either an infinite regular cardinalor is at most 3. Dually, the existence of a many-sorted terminal coalgebra implies that the iterative construction of a terminal coalgebra converges. Moreover, every endofunctor with a fixed-point pair larger than the number of sorts is proved to have aterminal coalgebra. As demonstrated by James Worell, the number of steps here need not be a cardinal even in the case of a single sort: it is omega + omega for the finite power-set functor. The above results do not hold for related categories, such as graphs: we present non-constructive initial algebras and terminal coalgebras.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)