@article{ADAMEK201841,
    Abstract = {This is a survey on fixed points of endofunctors, including initial algebras and terminal coalgebras. We also consider the rational fixed point, a canonical domain of behavior for finitely presentable systems. In addition to the basic existence theorems for fixed points, several new results are presented. For example, the Smyth--Plotkin theorem that locally continuous endofunctors of DCPO have terminal coalgebras is derived from a new result stating that every locally monotone endofunctor with a fixed point has a terminal coalgebra. We introduce bounded endofunctors on abstract categories and prove that they have terminal coalgebras. We study well-founded coalgebras and prove that for set functors, the largest well-founded coalgebra of every fixed point is the initial algebra. Another new result concerns mixed fixed points: initial algebras and terminal coalgebras of a parametrized accessible functor always form accessible functors.},
    Author = {Ad{\'a}mek, Ji{\v r}{\'\i} and Milius, Stefan and Moss, Lawrence S.},
    File = {Fixed points of functors - 1-s2.0-S2352220816301201-main - a.pdf},
    ISSN = {2352-2208},
    Journal = {Journal of Logical and Algebraic Methods in Programming},
    Keywords = {Fixed points of functors, Initial algebra, Terminal coalgebra, Rational fixed point},
    Pages = {41-81},
    Title = {Fixed points of functors},
    URL = {https://www.sciencedirect.com/science/article/pii/S2352220816301201},
    Volume = {95},
    Year = {2018},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2352220816301201},
    bdsk-url-2 = {https://doi.org/10.1016/j.jlamp.2017.11.003},
    date-added = {2023-03-11 22:48:55 +0100},
    date-modified = {2023-03-11 22:48:55 +0100},
    doi = {10.1016/j.jlamp.2017.11.003}
}

@article{ADAMEK201841, Abstract = {This is a survey on fixed points of endofunctors, including initial algebras and terminal coalgebras. We also consider the rational fixed point, a canonical domain of behavior for finitely presentable systems. In addition to the basic existence theorems for fixed points, several new results are presented. For example, the Smyth--Plotkin theorem that locally continuous endofunctors of DCPO have terminal coalgebras is derived from a new result stating that every locally monotone endofunctor with a fixed point has a terminal coalgebra. We introduce bounded endofunctors on abstract categories and prove that they have terminal coalgebras. We study well-founded coalgebras and prove that for set functors, the largest well-founded coalgebra of every fixed point is the initial algebra. Another new result concerns mixed fixed points: initial algebras and terminal coalgebras of a parametrized accessible functor always form accessible functors.}, Author = {Ad{\'a}mek, Ji{\v r}{\'\i} and Milius, Stefan and Moss, Lawrence S.}, File = {Fixed points of functors - 1-s2.0-S2352220816301201-main - a.pdf}, ISSN = {2352-2208}, Journal = {Journal of Logical and Algebraic Methods in Programming}, Keywords = {Fixed points of functors, Initial algebra, Terminal coalgebra, Rational fixed point}, Pages = {41-81}, Title = {Fixed points of functors}, URL = {https://www.sciencedirect.com/science/article/pii/S2352220816301201}, Volume = {95}, Year = {2018}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2352220816301201}, bdsk-url-2 = {https://doi.org/10.1016/j.jlamp.2017.11.003}, date-added = {2023-03-11 22:48:55 +0100}, date-modified = {2023-03-11 22:48:55 +0100}, doi = {10.1016/j.jlamp.2017.11.003} }