Il giorno lun, 01/06/2009 alle 16.15 +0300, Panagis Karazeris ha scritto:
Dear all, =20 I would like to announce that the following preprint is available as =20 http://arxiv.org/abs/0905.4883 =20 as well as from my webpage =20 www.math.upatras.gr/~pkarazer =20 Final Coalgebras in Accessible Categories, by Panagis Karazeris, Apostolos Matzaris and Jiri Velebil =20 Abstract: We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p= .) category and they bring an explicit construction of the final coalgebra= in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p. categories to which our results apply. We rely on ideas developed by Tom Leinster for the study of self-similar objects in topology.=20 =20 Best regards, Panagis Karazeris =20
I do not see the following paper in the references; would it be worth to provide a comparison? http://www.sciencedirect.com/science?_ob=3DArticleURL&_udi=3DB75H1-4G7MXP= F-4&_user=3D144492&_rdoc=3D1&_fmt=3D&_orig=3Dsearch&_sort=3Dd&view=3Dc&_a= cct=3DC000012038&_version=3D1&_urlVersion=3D0&_userid=3D144492&md5=3D5760= 58372d432ade83f476c43b8b466a Terminal sequences for accessible endofunctors=20 James Worrell Abstract: We consider the behaviour of the terminal sequence of an accessible endofunctor T on a locally presentable category K. The preservation of monics by T is sufficient to imply convergence, necessarily to a terminal coalgebra. We can say much more if K is Set, and =CE=BA is =CF=89= . In that case it is well known that we do not necessarily get convergence at =CF=89, however we show that to ensure convergence we don't need to go to= a higher cardinal, just to the next limit ordinal, =CF=89 + =CF=89. For an =CF=89-accessible endofunctor T on Set the construction of the terminal coalgebra can thus be seen as a two stage construction, with each stage being finitary. The first stage obtains the Cauchy completion of the initial T-algebra as the =CF=89-th object in the terminal sequence= A=CF=89. In the second stage this object is pruned to get the final coalgebra A=CF= =89 +=CF=89. We give an example where A=CF=89 is the solution of the correspo= nding domain equation in the category of complete ultra-metric spaces. Thanks Vincenzo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]